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
Find the area of both first. The sidewalk is 12 * 12 = 144 ft^2, and grass is 10 * 10 = 100 ft^2. Subtract the area of the grass from the sidewalk, 144-100 = 44 ft^2.
