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