# How do you write an equation of a line that goes through (-2,7) with m= -4?

May 25, 2015

The point-slope equation is $y - 7 = - 4 x - 8$, and the slope-intercept form is $y = - 4 x - 1$.

Use the point-slope form: $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $m$ is the slope and ${x}_{1}$ and ${y}_{1}$ are the known point.

Slope=$- 4$;
Point=$\left(- 2 , 7\right)$; ${x}_{1} = - 2$; ${y}_{1} = 7$

Substitute the known values into the equation.

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

y-7=-4(x-(-2) =

$y - 7 = - 4 \left(x + 2\right)$ =

$y - 7 = - 4 x - 8$

You can convert this into slope-intercept form, $y = m x + b$, by solving for $y$.

$y - 7 = - 4 x - 8$

Add $7$ to both sides.

$y = - 4 x - 1$