Answer:
y = - [tex]\frac{5}{3}[/tex] x - [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, 5) and (x₂, y₂ ) = (2, - 5) ← 2 points on the line
m = [tex]\frac{-5-5}{2+4}[/tex] = [tex]\frac{-10}{6}[/tex] = - [tex]\frac{5}{3}[/tex], thus
y = - [tex]\frac{5}{3}[/tex] x + b ← is the partial equation
To find b substitute either of the 2 points into the partial equation
Using (2, - 5), then
- 5 = - [tex]\frac{10}{3}[/tex] + b ⇒ b = - 5 + [tex]\frac{10}{3}[/tex] = - [tex]\frac{5}{3}[/tex]
y = - [tex]\frac{5}{3}[/tex] x - [tex]\frac{5}{3}[/tex] ← equation of line
