# Algebra 1 : How to find the equation of a perpendicular line

## Example Questions

### Example Question #21 : How To Find The Equation Of A Perpendicular Line

Suppose a line has an x-intercept of one and a y-intercept of two. What is the equation of the perpendicular line which pass through the point ?

Explanation:

Write the points that correspond to the x and y-intercepts given in the problem.

X-intercept of one:

Y-intercept of two:

Find the slope of this line connected with these points.

The slope is negative two. The slope of the perpendicular line is the negative reciprocal of this slope.

Write the slope-intercept form.

Substitute the perpendicular slope with the point that this line will pass through.

Solve for the y-intercept, .

Subtract nine halves on both sides.

Simplify both sides.

With the perpendicular slope and the y-intercept, write the equation of the line.

### Example Question #22 : How To Find The Equation Of A Perpendicular Line

What is the slope of a line perpendicular to the line with the following equation?

$3y+5x=9$

Answer cannot be determined from this information.

$\\3x+5y=9\rightarrow&space;\\\\&space;3y=-5x+9\rightarrow\\\\&space;y=-\frac{5}{3}x+3$
Next, we need to remember that perpendicular lines have slopes that are negative reciprocals. Find the negative reciprocal of $-\frac{5}{3}$:
$\frac{3}{5}$