Answer:
y = - [tex]\frac{3}{2}[/tex] x + 4
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 = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (6, - 5) and (x₂, y₂ ) = (- 8, 16)
m = [tex]\frac{16+5}{-8-6}[/tex] = [tex]\frac{21}{-14}[/tex] = - [tex]\frac{3}{2}[/tex], thus
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 8, 16), then
16 = 12 + c ⇒ c = 16 - 12 = 4
y = - [tex]\frac{3}{2}[/tex] x + 4 ← equation of line
