# How do you write the slope-intercept form of the equation of the line perpendicular to the graph of y=-3/2x-7 that passes through (3, -2)?

Mar 24, 2018

$y = \frac{2}{3} x - 4$

#### Explanation:

Slope-intercept form: y=mx+b where m is the slope and b is the y-intercept

First, let's find the slope of the equation. It is perpendicular to $y = - \frac{3}{2} x - 7$.

Perpendicular slopes are always opposite reciprocals of one another.

Opposites: positive vs. negative (-3 and 3 are opposites)

Reciprocals: numbers that multiply to 1 ($\frac{1}{3}$ and $3$ are reciprocals), flip the numerator and denominator of a number to find its reciprocal

Opposite of $- \frac{3}{2}$ is (positive) $\frac{3}{2}$

Reciprocal of $- \frac{3}{2}$ is $- \frac{2}{3}$

Opposite (positive) reciprocal of $- \frac{3}{2}$ is $\frac{2}{3}$

So far our equation is $y = \frac{2}{3} x + b$. We need to find the y-intercept.

Plug in the point that lies on this equation (3, -2)

$- 2 = \frac{2}{3} \cdot 3 + b$

$- 2 = 2 + b$

$b = - 4 \rightarrow$ This is the y-intercept

The equation is $y = \frac{2}{3} x - 4$