How do you write the equation in slope intercept form given y-(-4)=-1(x-6)?

Apr 28, 2016

$y = \left(- 1\right) x + 2$

Explanation:

Remember that the general slope-intercept form is
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} x + \textcolor{red}{b}$
for a line with slope $\textcolor{g r e e n}{m}$ and y-intercept $\textcolor{red}{b}$

Given
$\textcolor{w h i t e}{\text{XXX}} y - \left(- 4\right) = - 1 \left(x - 6\right)$

Add $\left(- 4\right)$ to both sides to isolate the $y$ on the left side
$\textcolor{w h i t e}{\text{XXX}} y = - 1 \left(x - 6\right) + \left(- 4\right)$

Simplify the right side
$\textcolor{w h i t e}{\text{XXX}} y = - x + 6 - 4$

$\textcolor{w h i t e}{\text{XXX")y=color(green)(} \left(- 1\right)} x + \textcolor{red}{2}$
which is the slope-intercept form
for a line with slope color(green)(""(-1)) and y-intercept $\textcolor{red}{2}$

Here is the graph of the original equation which supports our conclusion:
graph{y-(-4)=-1(x-6) [-4.27, 8.214, -2.124, 4.116]}