Answer:
y = - [tex]\frac{10}{3}[/tex] x - 23
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 9, 7 ) and (x₂, y₂ ) = (- 6, - 3 )
m = [tex]\frac{-3-7}{-6-(-9)}[/tex] = [tex]\frac{-10}{-6+9}[/tex] = [tex]\frac{-10}{3}[/tex] = - [tex]\frac{10}{3}[/tex] , then
y = - [tex]\frac{10}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 6, - 3 ) , then
- 3 = 20 + c ⇒ c = - 3 - 20 = - 23
y = - [tex]\frac{10}{3}[/tex] x - 23 ← equation of line
