Answer:
y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{10}{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 )
Calculate the slope m of H using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line
m = [tex]\frac{-2+3}{3-0}[/tex] = [tex]\frac{1}{3}[/tex]
Parallel lines have equal slopes, thus
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute (- 4, 2) into the partial equation
2 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = 2 + [tex]\frac{4}{3}[/tex] = [tex]\frac{10}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{10}{3}[/tex] ← equation of parallel line
