Question

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

$\mathit{y}\mathbf{-}\mathbf{2}\mathbf{=}\mathbf{3}\left(x-5\right)$

Short answer

The equation of the line in slope-intercept form is $\mathit{y}\mathbf{=}\mathbf{3}\mathit{x}\mathbf{-}\mathbf{13}$.

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.

The equation is given by,

$\begin{array}{c}y-2=3\left(x-5\right)\\ y-2=3x-15\\ y=3x-15+2\\ y=3x-13\end{array}$

This equation is in slope-intercept form $y=mx+b$, where$m=3$ and $b=-13$.

Therefore, the equation of the line in slope-intercept form is $y=3x-13$.