# Write an equation of a line parallel to 2y=4x-2, through the point (-3, 5)?

Mar 13, 2018

$y = 2 x + 11$

#### Explanation:

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

•color(white)(x)y=mx+b

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

$\text{rearrange "2y=4x-2" into this form}$

$\text{divide all terms by 2}$

$\Rightarrow y = 2 x - 1 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope } = m = 2$

• " Parallel lines have equal slopes"

$\Rightarrow {m}_{\text{parallel}} = 2$

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

$\text{to find b substitute "(-3,5)" into the partial equation}$

$5 = - 6 + b \Rightarrow b = 5 + 6 = 11$

$\Rightarrow y = 2 x + 11 \leftarrow \textcolor{red}{\text{equation of parallel line}}$