Question

Complete the equation of the line through (-8, -2) and (-4, 6)

Answer 1

Equation of line is given by:

`y=2x+14`

Explanation:

Given points:

`(-8,-2)\ and\ (-4,6)`

Slope of line
`m=(y_2-y_1)/(x_2-x_1)`

where
`(x_1,y_1)` and
`(x_2,y_2)` is a point on the line

`m=(6-(-2))/(-4-(-8))`

`m=(6+2)/(-4+8)`

`m=(8)/(4)`

∴
`m=2`

Point-slope equation of line is given by:

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

where
`(x_1,y_1)` is a point on the line and
`m` is slope of line.

Using point
`(-8,-2)` and slope
`m=2` point-slope equation of line is given by:

`y-(-2)=2(x-(-8))`

Simplifying.

`y+2=2(x+8)`

Using distribution.

`y+2=2x+16`

Subtracting 2 to both sides.

`y+2-2=2x+16-2`

`y=2x+14`

Thus, equation of line is
`y=2x+14`