Answer:
y = [tex]\frac{4}{3}[/tex] x + [tex]\frac{5}{3}[/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 )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, - 1) and (x₂, y₂ ) = (1, 3) ← 2 point on the line
m = [tex]\frac{3+1}{1+2}[/tex] = [tex]\frac{4}{3}[/tex] , then
y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 3 ), then
3 = [tex]\frac{4}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{4}{3}[/tex] = [tex]\frac{5}{3}[/tex]
y = [tex]\frac{4}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← equation of line
