Question

Write the given equation of line in slope-intercept form.

$\mathit{y}\mathbf{-}\mathbf{12}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{(}\mathit{x}\mathbf{-}\mathbf{3}\mathbf{)}$

Short answer

The equation of the line in slope-intercept form is$\mathit{y}\mathbf{=}\mathbf{-}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{18}$

Step-by-step solution

Step 1. Slope-intercept form of an equation of a line:

The slope-intercept form of an equation of a line is given by,

$y=mx+b$

Where, slope$=m$, and, $y-$axis intercept$=b$.

Step 2. Change the equation in slope-intercept form.

$\begin{array}{c}y-12=-2\left(x-3\right)\\ y-12=-2x+6\\ y=-2x+6+12\\ y=-2x+18\end{array}$

This equation is in slope-intercept form $y=mx+b$, where $m=-2$and $b=18$.

Therefore, the equation of the line in slope-intercept form is $y=-2x+18$.