What is the equation in point-slope form and slope intercept form for the line given (10,-9);m=-2?

May 23, 2015

The point-slope form is $y + 9 = - 2 \left(x - 10\right)$, and the slope-intercept form is $y = - 2 x + 11$.

Point-slope form: $y - {y}_{1} = m \left(x - {x}_{1}\right)$

Slope, $m = - 2$
Point, $\left(10 , - 9\right) = {x}_{1} , {y}_{1}$

Substitute the values for $m$, ${y}_{1}$, and ${x}_{1}$ into the equation..

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - \left(- 9\right) = - 2 \left(x - 10\right)$ =

$y + 9 = - 2 \left(x - 10\right)$

Slope-intercept form: $m x + b$

Solve $y + 9 = - 2 \left(x - 10\right)$ for $y$ .

Distribute the $- 2$.

$y + 9 = - 2 x + 20$

Subtract $9$ from both sides.

$y = - 2 x + 11$