Question

Complete the point-slope equation of the line through (-8,-8)(−8,−8)left parenthesis, minus, 8, comma, minus, 8, right parenthesis and (-7,9)(−7,9)left parenthesis, minus, 7, comma, 9, right parenthesis.

Use exact numbers.
y-9=y−9=y, minus, 9, equals

Answer 1

`y-9=17(x+7)`

Explanation:

Hi there!

What we know:

• The line goes through the points (-8,-8) and (-7,9)
• We need to write the equation of the line in point-slope form

What we need to know:

• Point-slope form:
  `y-y_1=m(x-x_1)` where m is the slope of the line and
  `(x_1,y_1)` is a point that the line passes through

• We're given "
  `y-9=`", which is the "
  `y-y_1`" part of the point-slope form equation. This means that
  `(x_1,y_1)` is
  `(-7,9)` and we only need to solve for m.

Our equation so far (plugging in the point (-7,9):

`y-9=m(x-(-7))`

`y-9=m(x+7)`

Determine the slope (m)

`m=(y_2-y_1)/(x_2-x_1)` where two points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (-8,-8) and (-7,9)

`=(-8-9)/(-8-(-7))\\=(-8-9)/(-8+7)\\=(-17)/(-1)\\= 17`

Therefore, the slope of the line is 17. Plug this into
`y-9=m(x+7)`:

`y-9=17(x+7)`

I hope this helps!