The parallel lines have the same slope. So we should check the slope from all the options. We will use formula m = (y₂ - y₁) / (x₂ - x₁)
First Option (x₁,y₁) = (-8,8) (x₂,y₂) = (2,2) Find the slope (m) m = (y₂ - y₁) / (x₂ - x₁) m = (2 - 8)/(2 + 8) m = -6/10 m = -3/5 It has the same slope of -3/5, so it's parallel with the line.
Second Option (x₁,y₁) = (-5,-1) (x₂,y₂) = (0,2) Find the slope (m) m = (y₂ - y₁) / (x₂ - x₁) m = (2 + 1) / (0 + 5) m = 3/5 It doesn't have the same slope, so it's not parallel with the line.
Third Option (x₁,y₁) = (-3,6) (x₂,y₂) = (6,-9) Find the slope (m) m = (y₂ - y₁) / (x₂ - x₁) m = (-9 - 6) / (6 + 3) m = -15/9 m = -5/3 It doesn't have the same slope, so it's not parallel with the line
Fourth Option (x₁,y₁) = (-2,1) (x₂,y₂) = (3,-2) Find the slope (m) m = (y₂ - y₁) / (x₂ - x₁) m = (-2 - 1) / (3 + 2) m = -3/5 It has the same slope of -3/5, so it's parallel with the line.
Fifth Option (x₁,y₁) = (0,2) (x₂,y₂) = (5,5) Find the slope (m) m = (y₂ - y₁) / (x₂ - x₁) m = (5 - 2) / (5 - 0) m = 3/5 It doesn't have the same slope, so it's not parallel with the line.
SUMMARY The parallel lines are first option and fourth option
