brian128282
contestada

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

Respuesta :

theleangreenbean

Answer:

[tex]y-9=17(x+7)[/tex]

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: [tex]y-y_1=m(x-x_1)[/tex] where m is the slope of the line and [tex](x_1,y_1)[/tex] is a point that the line passes through
  • We're given "[tex]y-9=[/tex]", which is the "[tex]y-y_1[/tex]" part of the point-slope form equation. This means that [tex](x_1,y_1)[/tex] is [tex](-7,9)[/tex] and we only need to solve for m.

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

[tex]y-9=m(x-(-7))[/tex]

[tex]y-9=m(x+7)[/tex]

Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

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

[tex]=\frac{-8-9}{-8-(-7)}\\=\frac{-8-9}{-8+7}\\=\frac{-17}{-1}\\= 17[/tex]

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

[tex]y-9=17(x+7)[/tex]

I hope this helps!