# How do you write the equation in point slope form given a line parallel to y= -2 + 3x passing through (-2,8)?

Nov 12, 2017

$y - 8 = 3 \left(x + 2\right)$

#### Explanation:

• " Parallel lines have equal slopes"

$y = 3 x - 2 \text{ is in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

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

$\Rightarrow y = 3 x - 2 \text{ has slope } m = 3$

$\text{hence a parallel line will have slope } m = 3$

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

•color(white)(x)y-y_1=m(x-x_1)

$\text{where m is the slope and "(x_1,y_1)" a point on the line}$

$\text{here "m=3" and } \left({x}_{1} , {y}_{1}\right) = \left(- 2 , 8\right)$

$y - 8 = 3 \left(x - \left(- 2\right)\right)$

$\Rightarrow y - 8 = 3 \left(x + 2\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$