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
