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Sep 12, 2024 · If a line runs perpendicular to another line, it means that it crosses it at a right angle and that you need to find its slope. The equation for a line on a graph is = +. The is the line, the is the slope of the line multiplied by , and the is where the line intercepts the y-axis of the graph.
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Find the equation of the line that is: parallel to y = 2x + 1; and passes though the point (5,4) The slope of y = 2x + 1 is 2. The parallel line needs to have the same slope of 2. We can solve it by using the "point-slope" equation of a line: y − y 1 = 2(x − x 1) And then put in the point (5,4): y − 4 = 2(x − 5) That is an answer!
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- Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel. Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees).
- Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. In other words,
- Through the point \((6, −1)\) we found a parallel line, \(y=\frac{1}{2}x−4\), shown dashed. Notice that the slope is the same as the given line, but the \(y\)-intercept is different.
- It is not always the case that the given line is in slope-intercept form. Often you have to perform additional steps to determine the slope.
Apr 26, 2021 · Find the rise over run (the slope) of the original line from its ???y???-intercept, then follow the rise over run pattern on the new ???y???-intercept and draw a point. Connect the points and draw the parallel line.
You can use these relationships to find an equation of a line that goes through a particular point and is parallel or perpendicular to another line. This page titled 13.2.3: Parallel and Perpendicular Lines is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by The NROC Project via source content that was edited to the style and standards of the LibreTexts platform.
How To: Given an equation for a line, write the equation of a line parallel or perpendicular to it. Find the slope of the given line. The easiest way to do this is to write the equation in slope-intercept form. Use the slope and the given point with the point-slope formula.
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In this tutorial, you will learn how to construct a line that is either parallel or perpendicular to a given reference line and passing through a fixed point. To be successful in solving this kind of problem, you need to have some background knowledge about the line itself. First: You should know how to find the slope of a line given two points.
