# How do you find equation of a line, L which passes through the point (3, -1) and parallel to the line which passes through the points (0,5) and (-2,-3)?

Jul 31, 2018

$y = 4 x - 13$

#### Explanation:

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

•color(white)(x)y=mx+c

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

$\text{calculate m using the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(0,5)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 2 , - 3\right)$

$m = \frac{- 3 - 5}{- 2 - 0} = \frac{- 8}{- 2} = 4$

• " Parallel lines have equal slopes"

$y = 4 x + c \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find c substitute "(3,-1)" into the partial equation}$

$- 1 = 12 + c \Rightarrow c = - 1 - 12 = - 13$

$y = 4 x - 13 \leftarrow \textcolor{red}{\text{equation of parallel line}}$