# Perpendicular Lines and Slope

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Perpendicular Lines and Slope

Perpendicular Lines A line is perpendicular to another if it meets or crosses at right angles (90°). For instance, a horizontal and a vertical line are perpendicular lines.

Slopes of Perpendicular Lines
Complete the following assuming Line A and Line B are perpendicular. Make Line A have a slope of What is the slope of Line B (the line perpendicular to Line A)? A B A B A B A B -3 2 2 3

Slopes of Perpendicular Lines
Two lines are perpendicular if their slopes are opposite reciprocals of each other. In other words, if the slope of a line is then the perpendicular line has a slope of Example: What is the slope of a line perpendicular to each equation below.

Note: The y-intercepts Normally are Not the Same
99.9% of the time, if two lines are parallel or perpendicular, they will NOT have the same y-intercept. (In fact, only RARELY do perpendicular lines share a y-intercept. If lines with the same slope have the same y-intercept, the lines coincide and are not parallel.)

Example Find the y-intercept.
Algebraically find the equation of the line that goes through the point (2,3) and is perpendicular to y = -4x – 2. This y-intercept does not matter. Find the y-intercept. Use Slope-Intercept Form: The slope is ¼ A point on the graph is x=2 and y=-3 The equation now has one distinct variable. Solve it. Substitute back into Slope-Intercept Form: