Answer:
lines are perpendicular to each other
Step-by-step explanation:
Parallel lines have equal slopes
The product of the slopes of perpendicular lines = - 1
Calculate the slopes of the lines using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } [/tex]
with (x₁, y₁ ) = (- 2, 1 ) and (x₂, y₂ ) = (3, 11 )
m = [tex]\frac{11-1}{3-(-2)} [/tex] = [tex]\frac{10}{3+2} [/tex] = [tex]\frac{10}{5} [/tex] = 2
Repeat with (x₁, y₁ ) = (0, 4 ) and (x₂, y₂ ) = (2, 3 )
m = [tex]\frac{3-4}{2-0} [/tex] = [tex]\frac{-1}{2} [/tex] = - [tex]\frac{1}{2} [/tex]
2 ≠ - [tex]\frac{1}{2} [/tex] , then lines are not parallel
2 × - [tex]\frac{1}{2} [/tex] = - 1 , then lines are perpendicular
