Answer:
y = 0
Step-by-step explanation:
Parallel lines have equal slopes
Calculate the slopes of both lines and equate them
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, - 3 ) and (x₂, y₂ ) = (3, y )
m = [tex]\frac{y-(-3)}{3-1}[/tex] = [tex]\frac{y+3}{2}[/tex]
Repeat with (x₁, y₁ ) = (5, - 6 ) and (x₂, y₂ ) = (9, y )
m = [tex]\frac{y-(-6)}{9-5}[/tex] = [tex]\frac{y+6}{4}[/tex]
Equating the 2 expressions
[tex]\frac{y+3}{2}[/tex] = [tex]\frac{y+6}{4}[/tex] ( cross- multiply )
4(y + 3) = 2(y + 6) ← distribute parenthesis on both sides
4y + 12 = 2y + 12 ( subtract 2y from both sides )
2y + 12 = 12 ( subtract 12 from both sides )
2y = 0 , then
y = 0
