# How do you write the slope-intercept equation for the line that is perpendicular to the line -5x + 2y = 16 and passes through the point (5, 7)?

Jun 30, 2017

Use the fact that slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.

Substitute the point into the slope-intercept form to find the value of b.

#### Explanation:

Given: $- 5 x + 2 y = 16$

$2 y = 5 x + 16$

Divide both sides by 2:

$y = \frac{5}{2} x + 8$

We can observe that the slope of the line $\frac{5}{2}$. The slope of a line that is perpendicular is the negative reciprocal, $- \frac{2}{5}$

The slope-intercept form is:

$y = - \frac{2}{5} x + b$

To find the value of b, substitute in the point $\left(5 , 7\right)$:

$7 = - \frac{2}{5} \left(5\right) + b$

$b = 9$

The equation is:

$y = - \frac{2}{5} x + 9$