# What is the y intercept for a line with point (6.-6) slope -7/3?

Sep 23, 2015

The y-intercept is $8$.

#### Explanation:

$y = m x + b$ is the slope-intercept form for a linear equation, where $m$ is the slope and $b$ is the y-intercept.

$x = 6 ,$ $y = - 6$

Substitute the known values for $x$ and $y$, and solve for $b$.

$- 6 = - \frac{7}{3} \cdot 6 + b =$

$- 6 = - \frac{42}{3} + b$

Simplify $- \frac{42}{3}$ to $- 14$.

$- 6 = - 14 + b$

Add $14$ to both sides of the equation.

$14 - 6 = b$

$8 = b$

Switch sides.

$b = 8$

The y-intercept is $8$.

The following graph has the slope-intercept equation $y = - \frac{7}{3} x + 8$

graph{y=-7/3x+8 [-19.96, 20.04, -4.39, 15.61]}