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

Answer:

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

Step-by-step 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)

$m=\frac{y_2-y_1}{x_2-x_1}$ where two points are $(x_1,y_1)$ and $(x_2,y_2)$

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

$=\frac{-8-9}{-8-(-7)}\\=\frac{-8-9}{-8+7}\\=\frac{-17}{-1}\\= 17$

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!