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
The question is asking how much time Susan spent moving toward her office. On the graph, the y-axis represents the distance Susan is from her office, so the amount of time she is moving toward her office is the amount of time the graph is going down.
As you can see, the graph is going down from the 10 to 16 minute marks and the 22 to 26 minute marks. In total, this is 20 minutes in which the graph is going down.
Therefore, Susan spends 20 minutes moving toward her office.
