Answer:
2x - 3y = 18
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 = - 3 into this form by subtracting 2x from both sides
- 3y = - 2x - 3 ( divide all terms by - 3 )
y = [tex]\frac{2}{3}[/tex] x + 1 ← in slope- intercept form
with slope m = [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes, thus
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
Given the y- intercept = 6, then
y = [tex]\frac{2}{3}[/tex] x + 6 ← equation in slope- intercept form
Multiply through by 3
3y = 2x + 18 ( subtract 3y from both sides )
0 = 2x - 3y + 18 ( subtract 18 from both sides )
2x - 3y = - 18 ← equation in standard form
