Question

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

$\mathit{y}\mathbf{-}\mathbf{4}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left(x+2\right)$

Short answer

The equation of the line in slope-intercept form is$\mathit{y}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{x}\mathbf{+}\mathbf{5}$

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,

$\begin{array}{c}y-4=\frac{1}{2}\left(x+2\right)\\ 2\left(y-4\right)=1\left(x+2\right)\\ 2y-8=x+2\\ 2y=x+2+8\\ 2y=x+10\\ y=\frac{x+10}{2}\\ y=\frac{x}{2}+\frac{10}{2}\\ y=\frac{1}{2}x+5\end{array}$

This equation is in slope-intercept form $y=mx+b$, where $m=\frac{1}{2}$and $b=5$.

Therefore, the equation of the line in slope-intercept form is $y=\frac{1}{2}x+5$.