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

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Answer 1 · 2015-05-11T03:54:27

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

Point-slope Form: $y - y_{1} = m (x - x_{1})$ $y-y_1=m(x-x_1)$ , where $(x_{1}, y_{1})$ $(x_1,y_1)$ is the given point and $m$ $m$ is the slope.

Point= $(5, 4)$ $(5,4)$
$m = - 5$ $m=-5$

$y - y_{1} = m (x - x_{1})$ $y-y_1=m(x-x_1)$ =

$y - 4 = - 5 (x - 5)$ $y-4=-5(x-5)$

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

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

Distribute the $- 5$ $-5$ .

$y - 4 = - 5 (x - 5)$ $y-4=-5(x-5)$ =

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

Add $4$ $4$ to both sides.

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

$y = - 5 x + 29$ $y=-5x+29$

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