# What is the equation in point-slope form and slope intercept form for the line given slope=-3 passing through (2,6)?

Apr 13, 2018

$y - 6 = - 3 \left(x - 2\right) , y = - 3 x + 12$

#### Explanation:

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

•color(white)(x)y-y_1=m(x-x_1)

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

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

•color(white)(x)y=mx+b

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

$\text{here "m=-3" and } \left({x}_{1} , {y}_{1}\right) = \left(2 , 6\right)$

$\Rightarrow y - 6 = - 3 \left(x - 2\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$

$\Rightarrow y - 6 = - 3 x + 6$

$\Rightarrow y = - 3 x + 12 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$