Answer:
A
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 + 4y = 8 into this form by adding 2x to both sides
4y = 2x + 8 ( divide all terms by 4 )
y = [tex]\frac{1}{2}[/tex] x + 2 ← in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Parallel lines have equal slopes, thus
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (- 5, - 1) into the partial equation
- 1 = - [tex]\frac{5}{2}[/tex] + c ⇒ c = - 1 + [tex]\frac{5}{2}[/tex] = [tex]\frac{3}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{2}[/tex] ← equation of parallel line
