# How do you write the equation of the line parallel to y=1/2x+6 and passes through (–8, 0)?

Dec 21, 2017

$y = \frac{1}{2} x + 4$

#### Explanation:

• " parallel lines have equal slopes"

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$y = \frac{1}{2} x + 6 \text{ is in this form}$

$\text{with } m = \frac{1}{2}$

$\text{hence equation of parallel line is}$

$y = \frac{1}{2} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(-8,0)" into the partial equation}$

$0 = - 4 + b \Rightarrow b = 4$

$\Rightarrow y = \frac{1}{2} x + 4 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$
graph{(y-1/2x-6)(y-1/2x-4)((x+8)^2+(y-0)^2-0.04)=0 [-10, 10, -5, 5]}