Answer: (7,-4)
Step-by-step explanation: The equation given is y + 4 = -5(x - 7). To determine which pair is located on the line represented by this equation, we need to substitute the values of x and y from each pair into the equation and check if the equation is satisfied.
Let's substitute the values from each pair into the equation:
1. For the pair (4, -7):
- Substituting x = 4 and y = -7 into the equation, we get:
-7 + 4 = -5(4 - 7)
-3 = -5(-3)
-3 = 15
- The equation is not satisfied, so the pair (4, -7) is not located on the line.
2. For the pair (-7, 4):
- Substituting x = -7 and y = 4 into the equation, we get:
4 + 4 = -5(-7 - 7)
8 = -5(-14)
8 = 70
- The equation is not satisfied, so the pair (-7, 4) is not located on the line.
3. For the pair (-4, 7):
- Substituting x = -4 and y = 7 into the equation, we get:
7 + 4 = -5(-4 - 7)
11 = -5(-11)
11 = 55
- The equation is not satisfied, so the pair (-4, 7) is not located on the line.
4. For the pair (7, -4):
- Substituting x = 7 and y = -4 into the equation, we get:
-4 + 4 = -5(7 - 7)
0 = -5(0)
0 = 0
- The equation is satisfied, so the pair (7, -4) is located on the line.
Therefore, the pair (7, -4) is the only pair located on the line represented by the equation y + 4 = -5(x - 7).
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