Answer:
y = - [tex]\frac{5}{9}[/tex] x - [tex]\frac{88}{9}[/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 )
Rearrange 5x + 9y + 18 = 0 into slope- intercept form
Subtract 5x + 18 from both sides
9y = - 5x - 18 ( divide all terms by 9 )
y = - [tex]\frac{5}{9}[/tex] x - 2 ← in slope- intercept form
with m = - [tex]\frac{5}{9}[/tex]
Parallel lines have equal slopes, thus
y = - [tex]\frac{5}{9}[/tex] x + c ← is the partial equation
To find c substitute (- 5, - 7) into the partial equation
- 7 = [tex]\frac{25}{9}[/tex] + c ⇒ c = - 7 - [tex]\frac{25}{9}[/tex] = - [tex]\frac{88}{9}[/tex]
y = - [tex]\frac{5}{9}[/tex] x - [tex]\frac{88}{9}[/tex] ← equation of line
