What is the equation in point-slope form and slope intercept form for the line given (9, 1) and (4, 16)?

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Answer 1 · 2015-05-20T23:33:12

The point-slope form is $y-1=-3(x-9)$ , and the slope-intercept form is $y=-3x+28$ .

Determine the slope, $m$ , using the two points.

Point 1: $(9,1)$
Point 2: $(4,16)$

$m=(y_2-y_1)/(x_2-x_1)=(16-1)/(4-9)=(15)/(-5)=-3$

Point-slope form.

General equation: $y-y_1=m(x-x_1)$ , where $x_1$ and $y_1$ are one point on the line. I will use Point 1: $(9,1)$ .

$y-1=-3(x-9)$

Slope-intercept form.

General equation: $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept.

Solve the point-slope equation for $y$ .

$y-1=-3(x-9)$

Distribute the $-3$ .

$y-1=-3x+27$

Add $1$ to each side.

$y=-3x+28$