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=(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=(-8-2)/(1-(-4))=(-10)/(1+4)=(-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":