# What is the equation of the line with slope -2/3 and passes through the point (3, 2)?

Jun 9, 2016

The equation of the line in slope-intercept form becomes

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

#### Explanation:

The slope intercept form of a line is $y = m x + b$

For this problem we are given the slope as $- \frac{2}{3}$ and a point on the line of $\left(3 , 2\right)$

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

We plug in the values and then solve for the $b$ term which is the
y-intercept.

$2 = - \frac{2}{3} \left(3\right) + b$

$2 = - 2 + b$

Now isolate the $b$ term.

$2 + 2 = \cancel{- 2} \cancel{+ 2} + b$

$b = 4$

The equation of the line in slope-intercept form becomes

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