Final answer:
The solution to the equation Y = -5/4x - 2 can be found by substituting the x and y values of each ordered pair into the equation. Only (-8, 8) satisfies the equation.
Step-by-step explanation:
To determine which ordered pairs are the solutions of the equation Y = -5/4x - 2, we can substitute the x and y values of each ordered pair into the equation and see if they satisfy the equation.
Let's check each option:
A. (-8, 8):
Substituting x = -8 and y = 8 into the equation, we get:
8 = -5/4(-8) - 2
8 = 10 - 2
8 = 8
So, (-8, 8) is a solution to the equation.
B. (8, -8):
Substituting x = 8 and y = -8 into the equation, we get:
-8 = -5/4(8) - 2
-8 = -10 - 2
-8 = -12
This does not satisfy the equation, so (8, -8) is not a solution to the equation.
C. (-8, 12):
Substituting x = -8 and y = 12 into the equation, we get:
12 = -5/4(-8) - 2
12 = 10 - 2
12 = 8
This does not satisfy the equation, so (-8, 12) is not a solution to the equation.
D. (1, -15/4):
Substituting x = 1 and y = -15/4 into the equation, we get:
-15/4 = -5/4(1) - 2
-15/4 = -5/4 - 2
-15/4 = -5/4 - 8/4
-15/4 = -13/4
This does not satisfy the equation, so (1, -15/4) is not a solution to the equation.
Therefore, the only ordered pair that is a solution of the equation Y = -5/4x - 2 is A. (-8, 8).