Question

What is an
equation of the line that passes through the points (-4, 2) and
(-8, -3)?

Answer 1

`y = 1(1)/(4)x+7`

Explanation:

The equation of a straight line can be written as
`y=mx+b`.

With the pair of coordinates (coordinates are written in the form
`(x,y)` ) , the following can be written:

`2=-4m+b`

`-3=-8m+b`

To solve for a variable, we can use elimination:

`-4m+b-(-8m+b)=2-(-3)` (subtract the second equation from the first)

`-4m+b+8m-b=2+3`

`4m=5` (
`b` is eliminated)

`m=(5)/(4)`

`=1(1)/(4)`

To solve for the other variable, we can use substitution:

`2=-4m+b`

`2=-4(1(1)/(4))+b`

`2 = -5 + b`

`b = 7`

`\therefore y=1(1)/(4)x+7` is the linear equation for the line that passes through the points
`(-4, 2)` and
`(-8,-3)`