Answer:
see explanation
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 ) = (- 3, - 1) and (x₂, y₂ ) = (3, 3)
m = [tex]\frac{3+1}{3+3}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex], thus
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 3), then
3 = 2 + c ⇒ c = 3 - 2 = 1
y = [tex]\frac{2}{3}[/tex] x + 1 ← equation of line
Multiply through by 3
3y = 2x + 3 ( subtract 3y from both sides )
0 = 2x - 3y + 3 ( subtract 3 from both sides )
- 3 = 2x - 3y, that is
2x - 3y = - 3 ← in standard form
