# How do you write the equation for the line (-14, -5) and parallel to the line determined by 6x + 7y = 28?

Jun 1, 2018

$y = - \frac{6}{7} x - 17$

#### 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

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

$\text{rearrange "6x+7y=28" into this form}$

$\text{subtract "6x" from both sides}$

$7 y = - 6 x + 28$

$\text{divide all terms by 7}$

$y = - \frac{6}{7} x + 4 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope } = - \frac{6}{7}$

$y = - \frac{6}{7} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(-14,-5)" into the partial equation}$

$- 5 = 12 + b \Rightarrow b = - 5 - 12 = - 17$

$y = - \frac{6}{7} x - 17 \leftarrow \textcolor{red}{\text{is equation of line}}$