Answer:
y = - [tex]\frac{7}{8}[/tex] x - [tex]\frac{3}{2}[/tex]
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 )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (-4, 2 ) and (x₂, y₂ ) = (4, - 5) ← 2 points on the line
m = [tex]\frac{-5-2}{4+4}[/tex] = - [tex]\frac{7}{8}[/tex]
y = - [tex]\frac{7}{8}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (4, - 5), then
- 5 = - [tex]\frac{7}{2}[/tex] + c ⇒ c = - [tex]\frac{3}{2}[/tex]
y = - [tex]\frac{7}{8}[/tex] x - [tex]\frac{3}{2}[/tex] ← in slope- intercept form
