Answer:
y = [tex]\frac{2}{3}[/tex] x - 9
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 )
Rearrange 2x - 3y = 6 into this form
Subtract 2x from both sides
- 3y = - 2x + 6 ( divide all terms by - 3 )
y = [tex]\frac{2}{3}[/tex] x - 2 ← in slope- intercept form
with m = [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes, thus
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (9, - 3) into the partial equation
- 3 = 6 + c ⇒ c = - 3 - 6 = - 9
y = [tex]\frac{2}{3}[/tex] x - 9 ← equation of line
