To determine which statements are true about the graph of the equation \( y = -4x + 7 \), we can plug in the x-coordinates from each of the coordinate pairs given in options A through E and see if the resulting y-value matches the y-coordinate of the pair.
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For (1, 3): \[ y = -4(1) + 7 = -4 + 7 = 3 \] This matches the y-coordinate, so A is true.
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For (2, 0): \[ y = -4(2) + 7 = -8 + 7 = -1 \] The result does not match the y-coordinate, so B is false.
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For (1, 4): \[ y = -4(1) + 7 = -4 + 7 = 3 \] The result does not match the y-coordinate, so C is false.
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For (0, 7): \[ y = -4(0) + 7 = 0 + 7 = 7 \] This matches the y-coordinate, so D is false (since it represents a point on the graph and is a solution to the equation).
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For (2, -2): \[ y = -4(2) + 7 = -8 + 7 = -1 \] Since the y-coordinate of this pair (-2) does not match the computed value (-1), E is true, as it does not represent a point on the graph or a solution to the equation.
Summary of Results:
- A: True
- B: False
- C: False
- D: False
- E: True
The true statements are A and E.