# How do you write an equation in slope intercept form of a line containing the coordinates (4,-5) with a slope of -6?

Jul 8, 2016

$y = - 6 x + 19$

#### Explanation:

With the point $\left(\textcolor{red}{4} , \textcolor{b l u e}{- 5}\right)$ and a slope of $\left(\textcolor{g r e e n}{- 6}\right)$
we can write the equation (initially) in slope-point form:
$\textcolor{w h i t e}{\text{XXX}} y - \left(\textcolor{b l u e}{- 5}\right) = \left(\textcolor{g r e e n}{- 6}\right) \left(x - \textcolor{red}{4}\right)$
then simplifying:
$\textcolor{w h i t e}{\text{XXX}} y + 5 = - 6 x + 24$
or
$\textcolor{w h i t e}{\text{XXX}} y = \left(\textcolor{g r e e n}{- 6}\right) x + \textcolor{p u r p \le}{19}$
which is the slope-intercept form with slope $\left(\textcolor{g r e e n}{- 6}\right)$ and y-intercept $\textcolor{p u r p \le}{19}$

graph{(-6x+19-y)((x-4)^2+(y+5)^2-0.01)=0 [-5.79, 14.21, -7.525, 2.475]}