# What is the y intercept for a line with point (12,-7) slope 5/2?

Oct 2, 2015

y-intercept: $\left(- 37\right)$

#### Explanation:

Step 1: Write equation in "point-slope form"
The point-slope form for a line with a slope of $m$ through a point $\left(\hat{x} , \hat{y}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$

For the given slope and point, this becomes
$\textcolor{w h i t e}{\text{XXX}} \left(y + 7\right) = \frac{5}{2} \left(x - 12\right)$

Step 2: Convert to "slope-intercept form"
The slope-intercept form for a line with slope $m$ and y-intercept $b$ is
$\textcolor{w h i t e}{\text{XXX}} y = m x + b$

Starting with
$\textcolor{w h i t e}{\text{XXX}} y + 7 = \frac{5}{2} \left(x - 12\right)$

$\textcolor{w h i t e}{\text{XXX}} y + 7 = \frac{5}{2} x - 30$

$\textcolor{w h i t e}{\text{XXX}} y = \frac{5}{2} x - 37$
which is the "slope-intercept form with y-intercept -37#