# High School Math : How to find the equation of a perpendicular line

## Example Questions

### Example Question #1 : Perpendicular Lines

Write an equation in slope-intercept form for the line that passes through and that is perpendicular to a line which passes through the two points and .     Explanation:

Find the slope of the line through the two points. It is .

Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula . Isolate for ### Example Question #29 : Algebra I

Find the equation of a line perpendicular to      Explanation:

Since a perpendicular line has a slope that is the negative reciprocal of the original line, the new slope is . There is only one answer with the correct slope.

### Example Question #30 : Algebra I

Find the equation (in slope-intercept form) of a line perpendicular to      Explanation:

First, find the slope of the original line, which is . You can do this by isolating for so that the equation is in slope-intercept form. Once you find the slope, just replace the in the original equation withe the negative reciprocal (perpendicular lines have a negative reciprocal slope for each other). Thus, your answer is ### Example Question #31 : Algebra I

Given the equation and the point , find the equation of a line that is perpendicular to the original line and passes through the given point.      Explanation:

In order for two lines to be perpendicular, their slopes must be opposites and recipricals of each other. The first step is to find the slope of the given equation:   Therefore, the slope of the perpendicular line must be . Using the point-slope formula, we can find the equation of the new line:   ### Example Question #31 : Algebra I

What line is perpendicular to through ?      Explanation:

Perdendicular lines have slopes that are opposite reciprocals.  The slope of the old line is , so the new slope is .

Plug the new slope and the given point into the slope intercept equation to calculate the intercept: or , so .

Thus , or .

### Example Question #1 : Perpendicular Lines

What is the equation, in slope-intercept form, of the perpendicular bisector of the line segment that connects the points and ?      Explanation:

First, calculate the slope of the line segment between the given points. We want a line that is perpendicular to this segment and passes through its midpoint. The slope of a perpendicular line is the negative inverse. The slope of the perpendicular bisector will be .

Next, we need to find the midpoint of the segment, using the midpoint formula. Using the midpoint and the slope, we can solve for the value of the y-intercept.    Using this value, we can write the equation for the perpendicular bisector in slope-intercept form. ### Example Question #2 : Perpendicular Lines

What line is perpendicular to through ?      Explanation:

The equation is given in the slope-intercept form, so we know the slope is .  To have perpendicular lines, the new slope must be the opposite reciprocal of the old slope, or Then plug the new slope and the point into the slope-intercept form of the equation: so so So the new equation becomes: and in standard form ### All High School Math Resources 