# What is the y intercept for a line with point (3,-5) slope -4/3?

Oct 1, 2015

y-intercept: $\left(- 1\right)$

#### Explanation:

"slope-point form" for a linear equation with slope $m$ through the point $\left(\hat{x} , \hat{y}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} y = m \left(x - \hat{x}\right) + \hat{y}$
For the given values this becomes
$\textcolor{w h i t e}{\text{XXX}} y = \left(- \frac{4}{3}\right) \left(x - 3\right) + \left(- 5\right)$

Simplifying
$\textcolor{w h i t e}{\text{XXX}} y = - \frac{4}{3} x + 4 - 5$
or
$\textcolor{w h i t e}{\text{XXX}} y = - \frac{4}{3} x - 1$
which is the "slope-intercept form"
with slope $= - \frac{4}{3}$
and
y-intercept $= - 1$