Which line is perpendicular to a line that has a slope of. Lines that are parallel to each other will never intersect.
Which line is perpendicular to a line that has a slope of Evaluate the options to determine which line has this slope. If you want to solve a problem in geometry quickly, give this perpendicular line calculator a try. Understand Perpendicular Slopes: Two lines are perpendicular if the product of their slopes is −1. For example, the figure below shows the graphs of various lines with the same slope, m = 2. It finds the equation of a (yet undefined) line that is perpendicular to a given line and passes through a given point. Sep 27, 2020 · Recognize that vertical lines have slopes that are undefined Identify slopes of parallel and perpendicular lines Given a line, identify the slope of another line that is parallel to it Given a line, identify the slope of another line that is perpendicular to it Interpret slope in equations and graphs Verify the slope of a linear equation given Nov 14, 2021 · In this section, we discuss parallel and perpendicular lines. Therefore, options B, C, and E are the correct choices. If it is negative, we say the line is decreasing. Thus, parallel and perpendicular slopes can be easily determined through these relationships. Parallel lines have the same slope, while perpendicular lines have slopes that are the opposite reciprocals of each other. A slope of 0 results in a horizontal line which we say is constant, and an undefined slope results in a vertical line. Study with Quizlet and memorize flashcards containing terms like Which point on the x-axis lies on the line that passes through point P and is perpendicular to line MN?, Lines RS, TV, and SW are shown. Our line also goes through the point (4,-1), so we'll write an equation with the point-slope formula. Oct 6, 2024 · To find which line is perpendicular to a line with a slope of −31, we need to determine the slope of a line that would be perpendicular to it. This means if one line has a slope m, the slope of the line that is perpendicular to it will be −m1 . Line SW has an undefined slope. . Parallel lines have the same slope and different y- intercepts. (True) Lines RS and TV are parallel because they have the same slope of 0. If two perpendicular lines cross, they will form four 90 degree angles. Jun 26, 2024 · The relationship between the slopes of perpendicular lines is a fundamental concept in geometry, which states that if two lines are perpendicular, the product of their slopes equals -1. This means if one line has a slope m, then Jun 11, 2024 · The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope. Whether you're tackling a school assignment or solving a geometric problem, this tool gives you the clarity and accuracy you need. Oct 23, 2024 · To find a line perpendicular to one with a slope of 21, we determine that the required slope is −2, which is the negative reciprocal. The concept of slope is one of the most fundamental concepts in geometry. If the green line has a slope of 52, what is the slope of the red line? Jun 23, 2016 · To find the slope of the red line which is perpendicular to the green line, we use the property that the product of the slopes of two perpendicular lines is -1. First, for reasons which will be made clear soon, if the slope is positive then the resulting line is said to be increasing. A perpendicular line will have a slope of −1, which is the negative reciprocal of the original slope. Jan 5, 2020 · The relationship between slopes of perpendicular lines is a fundamental concept in geometry, confirming that if the slope of one line is m1 , then the slope of the perpendicular line will be given by m2 =−m1 1 . Hence, without the slope of line a provided, we can't give a numerical value for the slope of line c (mc Oct 19, 2020 · To find a line that is perpendicular to a line with a given slope, we first need to understand the relationship between the slopes of two perpendicular lines. Nov 11, 2018 · Line k has a slope of −5. Recognize that vertical lines have slopes that are undefined Identify slopes of parallel and perpendicular lines Given a line, identify the slope of another line that is parallel to it Given a line, identify the slope of another line that is perpendicular to it Interpret slope in equations and graphs Verify the slope of a linear equation given Purplemath There is one other consideration for straight-line equations: finding parallel and perpendicular lines. This lesson explains how to find the slope of a line perpendicular to another line. The product of the slope of a given line and its perpendicular line is equal to -1. Oct 7, 2020 · The slope of line c is 1, as it is parallel to line b, which also has a slope of 1. Free line equation calculator - find the equation of a line given two points, a slope, or intercept step-by-step Study with Quizlet and memorize flashcards containing terms like Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)? line AB line CD line FG line HJ, A line has a slope of . If line m is parallel to line k, then it has a slope of, Which of the following pairs of slopes are of perpendicular lines? and more. To determine which line has this slope, we would need the slopes of lines AB Example Calculation: If line A has a slope of 3, the slope of line B (perpendicular to A) would be -1/3. For example, the figure below shows the graphs of various lines with the same slope, m = 2 m = 2. Feb 20, 2010 · This tutorial looks at the relationship between the slopes of parallel lines as well as perpendicular lines. Find the negative reciprocal of the given slope: The slope Apr 2, 2018 · To find a line perpendicular to a slope of 21, its slope must be −2. Perpendicular lines have slopes that are opposite reciprocals, so the slope of our line is the opposite reciprocal of -4/3, or 3/4. Dec 21, 2016 · The slope of the line y = x − 4 is 1, hence any parallel line will also have a slope of 1. Remember, perpendicular lines have slopes that are negative reciprocals of one another. Sep 9, 2024 · Sure, let's solve this step-by-step! To determine which line is perpendicular to a line with a slope of 21, we need to understand the relationship between the slopes of perpendicular lines. Free line equation calculator - find the equation of a line given two points, a slope, or intercept step-by-step Parallel lines are any lines that have the same slope. However, with the information provided, we established the necessary perpendicular slope. \nonumber \] Oct 24, 2022 · The slope of a line perpendicular to line ℓ, which has a slope between 0 and 1, will be less than -1. 7 hours ago · After carefully analyzing the coordinates of points P, Q, and R from the graph, calculating the slope of line PQ, determining the slope of a line perpendicular to PQ, and deriving the equation of the line passing through point R with the perpendicular slope, we find that none of the provided options satisfy the equation. Here is a common format for exercises on this topic: Given the line 2x − 3y = 9 and the point (4, −1), find lines, in slope-intercept form, through the given point such that the two lines are, respectively,: Study with Quizlet and memorize flashcards containing terms like Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)? line AB line CD line FG line HJ, A line has a slope of . Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. Oct 3, 2024 · So, the slope of the line that is perpendicular to the original line is 3. and more. This means that the inequality for the slope of the perpendicular line is expressed as m₂ < -1. Which ordered pairs could be points on a line that is perpendicular to this line? Feb 20, 2010 · This tutorial looks at the relationship between the slopes of parallel lines as well as perpendicular lines. Find the Perpendicular Slope: For two lines to be perpendicular, the product of their slopes must be −1. In this post, we will discuss the different ways to determine the slopes of perpendicular lines. Recognize that vertical lines have slopes that are undefined Identify slopes of parallel and perpendicular lines Given a line, identify the slope of another line that is parallel to it Given a line, identify the slope of another line that is perpendicular to it Interpret slope in equations and graphs Verify the slope of a linear equation given Nov 23, 2020 · The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the original line. Perpendicular lines have slopes that multiply to -1, which helps in finding the perpendicular slope easily. Nov 21, 2023 · Slope, also called the gradient or rate of change, is a value that describes how steep a line is and the direction of the line. Slope = undefined x = 3 Parallel line slope y = 2x + 3 and y = 2x - 4 both have a slope of 2, so they are parallel, as shown below: Perpendicular line slope Perpendicular lines have slopes that are "opposite reciprocals" of each other. Which ordered pairs could be points on a line that is perpendicular to this line? Master the concept of the slope of a line! This guide provides a clear definition calculation methods and illustrative examples. Apr 2, 2018 · To find a line perpendicular to a slope of 21, its slope must be −2. These two lines are perpendicular, but the product of their slopes is not –1. Apr 2, 2025 · Example 4 6 4 Find the equation of the line shown. To find a line perpendicular to a line with a given slope, we need to use the property that the product of the slopes of two perpendicular lines is -1. Slope is used in algebra to find the angle or steepness of the line A line that is perpendicular to another will have a slope that is the negative reciprocal of the other line's slope. Nov 12, 2025 · If we take a closer look at these two lines, the slope of one is -4 and the other is 1/4. Jan 23, 2025 · A line that is perpendicular to a line with a slope of −31 has a slope of 3. It describes the steepness of line in the coordinate plane. Jun 16, 2020 · For example, if a line has a slope of 2, then a line that is perpendicular to it will have a slope of -\frac {1} {2} because they are negative reciprocals of each other. Sep 27, 2020 · A perpendicular line will have a slope that is the negative reciprocal of the slope of y = 3, but what does that mean in this case? The reciprocal of 0 is 1 0, but we know that dividing by 0 is undefined. The calculation of slopes could be based on their coordinates or equations defined in the question. Oct 28, 2025 · Slope calculator finds slope of a line using the formula m equals change in y divided by change in x. Which statements are true about these lines? Check all that apply. Mar 21, 2025 · Understand Perpendicular Slopes: For two lines to be perpendicular, the slope of one line must be the negative reciprocal of the slope of the other line. Without specific slope information for lines AB,C D,FG, or H J, we Feb 19, 2018 · The slope or a line perpendicular to another line is the negative reciprocal of the first line. Solution We need to find the slope and y -intercept of the line from the graph so we can substitute the needed values into the slope–intercept form, y = m x + b. Feb 12, 2025 · Let’s start with an example. com Slope of the perpendicular line can be obtained from the product of the slope of two lines. Now, let's analyze the given options by calculating their slopes: The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = 1/6 is a vertical line with a slope that is undefined. Perpendicular lines aren’t present in all shapes, although they’re always found in squares, right-angled triangles, and rectangles. Mar 19, 2020 · A line perpendicular to one with a slope of −31 has a slope of 3. This property is due to the definition of perpendicular lines in a coordinate plane, where the product of their slopes is -1. Feb 1, 2025 · A line is perpendicular to another if it has a slope that is the negative reciprocal of the original line's slope. Check the slopes of the provided lines to determine which one meets that criterion. For example, the figure above shows the graph of two Sep 2, 2024 · Finding Equations of Parallel and Perpendicular Lines We have seen that the graph of a line is completely determined by two points or one point and its slope. When two lines intersect at right angles, they are perpendicular lines, and we can measure their slope. Jun 10, 2022 · To determine which line is perpendicular to a line with a slope of −65, we need to find the slope of the perpendicular line. The slopes of two perpendicular lines, denoted as m₁ and m₂, satisfy the equation: If the slope of the first equation is 4, then the slope of the second equation will need to be 1 4 for the lines to be perpendicular. This means that the slope of the perpendicular line is the negative reciprocal of the original line's slope. Perpendicular lines are two or more lines that intersect at a -degree angle, like the two lines drawn on this graph, and the - and -axes that orient them. See full list on mathsisfun. Nov 11, 2018 · The correct option is line EF. Thus, no pairs are correct as per the given options. Study with Quizlet and memorize flashcards containing terms like Parallel lines have the same slope. Aug 24, 2022 · Lines with a larger positive slope should rise more quickly than lines with a smaller positive slope. To see if a pair of points defines a line perpendicular to the given line, calculate the slope using the formula (y2 - y1) / (x2 - x1) and check for equality with -3/2. This relationship is fundamental in determining line orientation in coordinate geometry. The slope of the given line is -\frac {1} {2}. May 2, 2022 · A horizontal line has a slope of zero and a vertical line has an undefined slope. Find the equation of a line that passes through the point (1, 7) and is perpendicular to the line y = 4 x 3. Jul 20, 2017 · To find the slope of the red line, which is perpendicular to the green line, we use the relationship between the slopes of perpendicular lines. Lines that are parallel to each other will never intersect. Given a point and a line perpendicular to or parallel to the unknown line, write the equation of the unknown line. Example Write the equation of the line that has a slope of 1 2 and a y -intercept of 5. Jul 31, 2024 · To find a line perpendicular to one with a slope of 21, we need a line that has a slope of −2. Perpendicular lines have slopes that are negative reciprocals of each other. Given line A and point P, Sal finds the equation of the line perpendicular to A that passes through P. Calculating the slope of a line is similar to finding the slope between two different points. The equation point slope calculator will find an equation in either slope intercept form or point slope form when given a point and a slope. Line TV has a slope of 0. The slope of a line perpendicular to this would be the negative reciprocal, which is -5/3. At this point, to determine which line (among line MN, line AB, line EF, and line JK) is perpendicular, you would need additional information about the slopes of those specific lines. Create the equation for line j. A line with a slope of 0 is a horizontal line. So, for the line with a slope of -\frac {1} {3}, the slope of the perpendicular line is indeed 3, corroborating our answer. In general, to find the slope of a line, we need to have the values of any two different coordinates on Jan 23, 2024 · To find the slope of a line perpendicular to the given line 3x - 5y = 8, we first determine the slope of the original line, which is 3/5. Aug 23, 2018 · A perpendicular line has a negative reciprocal of a given line. Let's say you have a line with slope 6; the slope of the perpendicular line is -1/6. Nov 2, 2022 · The slope of the other line is −2, as it is the negative reciprocal of the slope 21 of the first line. Parallel and Perpendicular Lines Learning Objectives Find the slope of a line that is parallel or perpendicular to an existing line. However, none of the provided options yield ordered pairs that fit this criterion. The slope-intercept equation of a line is y = mx + b, where x and y identify a point, m is the slope, and b is y-intercept. Introduction Perpendicular linesLines that have opposite reciprocal slopes. However, without the slope information for lines MN, AB, EF, or JK, we cannot determine which line is perpendicular. It's important to verify the relationships between the slopes for statements D and E to be confident about their truths. If two lines have negative slope, then the line having the slope with larger absolute value should fall more quickly than the other line. We can find an equation of the line which is perpendicular to the other. A linear equation in two variables, written as y = m x + q, expresses a direct relationship between x and y. Lines RS and TV are parallel. If the slope of the first equation is 4, then the slope of the second equation will need to be 1 4 for the lines to be perpendicular. Study with Quizlet and memorize flashcards containing terms like What is the slope of line PQ? What is the slope of line MN? How are the two lines related?, Which line is perpendicular to a line that has a slope of -1/3?, Which points could be on the line that is parallel to and passes through point J? Check all that apply. When dealing with slope, the negative reciprocal allows us to determine the slope of a line that is perpendicular to another. Free perpendicular line calculator - find the equation of a perpendicular line step-by-step Nov 21, 2023 · Learn about perpendicular lines and the slope of a perpendicular line. This can be generalized to any pair of perpendicular lines in the coordinate plane. The relationship between the slopes of two perpendicular lines is that the product of their slopes is −1. Apr 16, 2021 · Finding Equations of Parallel and Perpendicular Lines We have seen that the graph of a line is completely determined by two points or one point and its slope. , Line k has a slope of 2/3. Aug 8, 2017 · The lines shown below are perpendicular. Instructions: Use this graphing tool to plot the find, step-by-step, the slope of a perpendicular line to a line that has a given slope. If you need a review on these concepts, feel free to go to Tutorial 26 A horizontal line has a slope of zero and a vertical line has an undefined slope. Apr 2, 2024 · The slope of the lines differs because the slope of one line is the negative reciprocal of the slope of the other. A horizontal line has slope 0, and the negative reciprocal of zero is undefined (division by zero). Among the options, line AB has this slope. The slope of a line that is perpendicular to another line with a slope of −m will be the negative reciprocal, which means it will have a slope of m1. Line b is perpendicular to line a, confirming the relationship between the lines. You can also check the two slopes to see if the lines are perpendicular by multiplying the two slopes together. Mar 3, 2025 · To determine which ordered pairs could lie on a line that is perpendicular to a given line with a slope of −54, we should first understand the concept of perpendicular slopes. Jul 11, 2024 · To determine which line is perpendicular to a line that has a slope of −31, we need to understand the relationship between slopes of perpendicular lines. Any line that moves upwards as it goes further to the right is positive. Dec 15, 2024 · Learning Objectives Find the slope of a line that is parallel or perpendicular to an existing line. For a line with a slope of 21, the negative reciprocal is −2. Jun 12, 2018 · To find a line that is perpendicular to a line with a slope of 65, we first need to understand the relationship between the slopes of two perpendicular lines. Additionally, it calculates the coordinates of the intersection point of the two lines. Solution We need to find the slope and y -intercept of the line from the graph so we can substitute the needed values into the slope-intercept form, y = m x + b. This means if the slope of one line is m, the slope of the line that is perpendicular to it will be −m1 May 16, 2025 · They are perpendicular if their slopes are negative reciprocals m r = 1 m s The slope ( m ) is undefined for lines parallel to the y-axis, and equal to 0 for lines parallel to the x-axis. Understanding Slopes of Perpendicular Lines: Jan 2, 2017 · If line b is perpendicular to line a, and line c is perpendicular to line a, then both lines b and c have slopes that are the negative reciprocal of line a's slope. Perpendicular lines are everywhere, not just on graph paper but also in the world around us, from the crossing pattern of roads at an intersection to the colored lines of a plaid shirt. Jan 11, 2023 · Learn how to find the perpendicular slope. Apr 17, 2025 · For example, if Line AB has a slope of 1, Line FG has a slope of −21, and Line HJ has a slope of −2, then Line HJ would be the perpendicular line to the one with slope 21. Explore the formula for finding the slopes with examples and practice problems. Therefore, lines like y = 3x or y = 3x −1 are perpendicular to the given line. The slope of perpendicular lines is the negative reciprocal of other lines. An example of such a line could be described by the equation y = 3x + b. A perpendicular line will have a slope that is the negative reciprocal of the slope of y = − 3, but what does that mean in this case? This means that we are looking for a line whose slope is undefined, and we also know that vertical lines have slopes that are undefined. Perpendicular lines are lines that become parallel when one is rotated 90 degrees. Therefore, the slope of line c remains consistent at 1. Then a line perpendicular to one that has a** slope **of -1/3 must have a **slope **of 3. Because a horizontal line (parallel to x-axis) has a slope of 0, and the line perpendicular to that will a vertical line (parallel to y-axis) and has an undefined slope. The given slope is 1/3, the reciprocal of this would be 3/1, which simplifies to 3. Therefore, more information is needed to answer the question. Apr 18, 2020 · This step-by-step guide will teach you how to graph parallel lines and perpendicular lines using slope! The guide includes several examples of how to find the slopes of parallel and perpendicular lines (and how to graph them). Learn how to find them using equations, view them on a graph, and take a quiz. Jun 10, 2020 · The question asks for points on a line that is perpendicular to a line with a slope of -1 (which would require a slope of +1). Jun 25, 2021 · D. The negative of 3 is -3. , Line WV is perpendicular to both line RS and line TU. Jun 16, 2019 · Upload your school material for a more relevant answer To find a perpendicular line to one with a slope of -5/6, calculate the negative reciprocal, which is 6/5. We can show that two lines are perpendicular if the product of the two slopes is 1: m 1 m 2 = 1. Perpendicular lines will have a slope equal to the negative inverse of the known slope. Here, we have to use our intuition. In this case, the negative reciprocal of 21 is −2. Please provide the slope of your line (any valid numeric expression). Therefore, line AB is the correct answer. The equation of a perpendicular line to must have a slope that is the negative reciprocal of the original slope. Oct 17, 2020 · To determine the relationship between line TU and line RS, we first need to calculate their slopes since parallel and perpendicular lines have specific relationships with their slopes. The y -intercept is (0,−4) and the graph passes through (3,−2). It is used to calculate the steepness and direction of a line, which can then be used to identify other properties of a line or figure. Learn how to construct a line, parallel or perpendicular, to a given reference line and a fixed point, and in the process learn how to utilize the Point-Slope Form and Slope-Intercept Form of a Line. Aug 31, 2023 · Find the slope of a line Graph a line given a point and the slope Graph a line using its slope and intercept Choose the most convenient method to graph a line Graph and interpret applications of slope–intercept Use slopes to identify parallel and perpendicular lines Compare parallel and perpendicular lines with examples in this 5-minute video. E. Feb 26, 2024 · Explanation Perpendicular lines have slopes that are negative reciprocals. So, to determine the slope of the line we are looking for, we must first determine the slope of the line we are given. (True) Line SW is vertical and perpendicular to both horizontal lines RS and TV. Sep 24, 2024 · To determine which line is perpendicular to a line that has a slope of −65, follow these steps: Understand the concept of perpendicular slopes: Two lines are perpendicular to each other if the product of their slopes is −1. Therefore, the correct option is B. All of the lines shown in the graph are parallel because they have the same slope and different y- intercepts. May 14, 2025 · The Perpendicular Line Calculator offers a quick, easy way to find perpendicular lines and understand slope relationships. The chosen answer will be the line with a slope of 6/5. The answer is a) -3. are two or more lines that intersect at a `90` -degree angle, like the two lines drawn on this graph, and the `x` - and `y` -axes that orient them. \nonumber \] Jun 29, 2025 · Definition: Slope-Intercept Form of a Line The slope-intercept form of the line with slope \ (m\) and y-intercept \ ( (0, b)\) is the equation\ [y = mx + b. In this context, "opposite" refers to the change in sign from + to - or vice versa. You will need to know how to find the slope of a line given an equation and how to write the equation of a line. All you have to do is input the coordinates of any point and the coefficients describing Jul 1, 2025 · A few comments about Example \ ( \PageIndex {1} \) are in order. Jul 31, 2020 · The slope of a line perpendicular to a line with a slope of 4 is −41. The y -intercept is (0, 4) and the graph passes through (3, 2). Oct 25, 2024 · To find a line that is perpendicular to a line with a slope of −31, we look for a line with a slope of 3, the negative reciprocal of −31. When two lines are perpendicular, their slopes multiply to −1. Once again we are going to be using material from our math past to help find the new concept. Which statement must be true about line TU? and more. Let's see how to get that solution: First, we know that two** lines are perpendicular if the slope of one is equal to the opposite **of the **inverse of the opposite **of the other. Sep 5, 2017 · The line that is perpendicular to another line with a slope of 21 has a slope of −2. Sep 10, 2020 · The perpendicular line is line EF. Oct 1, 2020 · The true statements about the lines are that line SW has an undefined slope, line TV has a slope of 0, and line SW is perpendicular to line RS. Often you will be asked to find the equation of a line given some geometric relationship—for instance, whether the line is parallel or perpendicular to another line. The slopes of perpendicular lines are opposite reciprocals of each other. Jun 16, 2022 · The line perpendicular to a given line with a slope of 2/3 will have a slope of -3/2. Therefore, the slope of the line that is perpendicular to a line with a slope of -4/5 is: To determine which pair of points could lie on the perpendicular line, substitute their coordinates into the slope formula. Identify the Slope: The slope of the given line is 21 . Among the options provided, if line CD has a slope of −2, that would be the answer. To find the slope, we choose two points on the graph. The relationship of slopes helps establish these truths about the lines' orientations. Line j is perpendicular to line k and passes through the point (5,9). If the slope of one line is m1, then the slope of a line that is perpendicular to it, m2, can be found using the formula: Jul 22, 2020 · The true statements about the lines are likely A (the slope of line MN is 32), B (the slope of line PQ is undefined), and C (the slope of line RS is −23). The slope of one line is the negative reciprocal of the other. Since parallel lines have the same slope, we now know that the slope of a line parallel to 8 x − 5 y = 10 is also 8 5. Discover the equation of lines and how to find the slope of a perpendicular Jun 14, 2022 · Using Slope to Identify Parallel and Perpendicular Lines Compare the equations of two lines and identify whether they are parallel or perpendicular. What is slope? The slope of the line is the ratio of the rise to the run, or rise divided by the run. It covers the concept of negative reciprocal slopes and provides step-by-step instructions with examples. Jun 29, 2025 · Definition: Slope-Intercept Form of a Line The slope-intercept form of the line with slope \ (m\) and y-intercept \ ( (0, b)\) is the equation\ [y = mx + b. However, specific slopes for each line are needed to confirm the answer. Lines that are perpendicular intersect to form a 90 ∘ -angle. Shows the work, graphs the line and gives line equations. The calculator also has the ability to provide step by step solutions. A horizontal line has a slope of zero and a vertical line has an undefined slope. The relationship between parallel lines and between perpendicular lines is unique, where the slope will be most interesting to us in this section. The concept of a negative reciprocal is crucial for understanding perpendicular lines and certain transformations in algebra and geometry. May 21, 2017 · A line perpendicular to the graph of the line would have a slope of perpendicular lines must have the same angle, then perpendicular lines have the same slope with negative sign. What if you were given two perpendicular lines in the coordinate plane? What could you say about their slopes? Jul 2, 2024 · Example 3 4 4 Find the equation of the line shown in the graph. jjwb dbjg vidzv ptbz risvpygla mfnrojk glesey qouf vbcr wzmsvn mcgnqp tnz ambaid etat lvbqjz