Question

Complete the point-slope equation of the line through (-8,-1) and (-6,5).

Use exact numbers.
y-5=

Answer 1

The completed slope point equation is
`y=3x+23`

Explanation:

Given points are (-8,-1) and (-6,5)

Now to find the slope with these points

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the points (-8,-1) and (-6,5) respectively

Substitute all values in
`m=(y_(2)-y_(1))/(x_(2)-x_(1))` we get

`m=(5-(-1))/(-6-(-8))`

`=(5+1)/(-6+8)`

`=(6)/(2)`

`=3`

Therefore m=3

Now to find the equation:

`y-y_(1)=m(x-x_(1))`

Let
`(x_(1),y_(1))` be the point (-6,5)

Substitute the point (-6,5) and slope m=3

`y-5=3(x-(-6))`

`y-5=3(x+6)`

`y-5=3x+18`

`y=3x+18+5`

`y=3x+23`

Therefore the completed slope point equation is
`y=3x+23`