What is the equation in point-slope form and slope intercept form for the line given (5,4), m=-5?

May 11, 2015

The point-slope form is $y - 4 = - 5 \left(x - 5\right)$, and the slope-intercept form is $y = - 5 x + 29$ .

Point-slope Form: $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $\left({x}_{1} , {y}_{1}\right)$ is the given point and $m$ is the slope.

Point=$\left(5 , 4\right)$
$m = - 5$

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

$y - 4 = - 5 \left(x - 5\right)$

Slope-intercept Form: $y = m x + b$, where $m$ is the slope, and $b$ is the y-intercept.

Solve $y - 4 = - 5 \left(x - 5\right)$ for $y$ .

Distribute the $- 5$.

$y - 4 = - 5 \left(x - 5\right)$ =

$y - 4 = - 5 x + 25$

Add $4$ to both sides.

$y = - 5 x + 25 + 4$ =

$y = - 5 x + 29$

The slope is $- 5$ and the y-intercept is $29$.