Question

Find an equation of the line between (-4,2) and (1,-8)

Answer 1

Given the points:

$\mleft(-4,2\mright),(1,-8)$

You can find the slope of the line using this formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where these two points are on the line:

$(x_1,y_1),(x_2,y_2)$

In this case, you can set up that:

$\begin{gathered} y_2=-8 \\ y_1=2 \\ x_2=1 \\ x_1=-4 \end{gathered}$

Therefore:

$m=\frac{-8-2}{1-(-4)}=\frac{-10}{1+4}=\frac{-10}{5}=-2$

By definition, the Slope-Intercept Form of the equation of a line is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

In order to find the y-intercept, substitute the slope and the coordinates of one of the points on the line into the equation, and then solve for "b":

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