Answer:
y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{17}{4}[/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 slope formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (- 9, 2)
m = [tex]\frac{2-5}{-9-3}[/tex] = [tex]\frac{-3}{-12}[/tex] = [tex]\frac{1}{4}[/tex]
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
using (3, 5), then
5 = [tex]\frac{3}{4}[/tex] + c ⇒ c = 5 - [tex]\frac{3}{4}[/tex] = [tex]\frac{17}{4}[/tex]
y = [tex]\frac{1}{4}[/tex] x +[tex]\frac{17}{4}[/tex] ← in slope- intercept form
