Answer:
y = [tex]\frac{8}{3}[/tex] x + [tex]\frac{1}{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 )
y = [tex]\frac{8}{3}[/tex] x + 2 ← is in slope- intercept form
with slope m = [tex]\frac{8}{3}[/tex]
Parallel lines have equal slopes , thus
y = [tex]\frac{8}{3}[/tex] x + c ← is the partial equation
To find c substitute (- 2, - 5) into the partial equation
- 5 = - [tex]\frac{16}{3}[/tex] + c ⇒ c = - 5 + [tex]\frac{16}{3}[/tex] = [tex]\frac{1}{3}[/tex]
y = [tex]\frac{8}{3}[/tex] x + [tex]\frac{1}{3}[/tex] ← equation of parallel line
