Point Slope Form

$\fcolorbox{#00BFFF}{white}{$y-y_1=m(x-x_1)$}$

$\fcolorbox{#00BFFF}{white}{$y-y_1=m(x-x_1)$}$\fcolorbox{#00BFFF}{white}{$y-y_1=m(x-x_1)$}

Goal:

Using point-slope form write an equation of the line through a given point and the slope.

Definition:

m = slope

$(x_1, y_1)$

Assuming that the line has a slope guarantees that it is not vertical.  The point-slope form is helpful when we have a slope and a point given to us.

Example:

Write an equation of the line through (5, 4) having a slope of 2.

Steps:

Since we know the following we can label and plug them in.

$m=2$m=2

$x_1 = 5$

$y_1= 4$

$y-y_1=m(x-x_1)$

$y_1 = 4$y_1 = 4

$y-y_1=m(x-x_1)$y-y_1=m(x-x_1)

$y-4=2(x-5)$y-4=2(x-5)

$y-4=2x-10$y-4=2x-10

$\colorbox{aqua}{$y=2x-6$}$\colorbox{aqua}{$y=2x-6$}

Good work!



By: Ed

Sept. 4, 2020