To evaluate which of the statements A, B, C, or D is true regarding the equation \( y = \frac{1}{4}x - 3 \), let's analyze each of the provided points:
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Statement A: (12, 0) is a solution to the equation but is not a point on the graph.
- Substitute \( x = 12 \) into the equation: \[ y = \frac{1}{4}(12) - 3 = 3 - 3 = 0 \] Thus, the point \( (12, 0) \) is indeed a solution to the equation.
- However, since this point gives a correct \( y \)-value and it corresponds to an \( x \) value we just calculated, it is also on the graph. Hence, this statement is false.
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Statement B: (0, 1.5) is a solution to the equation and is a point on the graph.
- Substitute \( x = 0 \) into the equation: \[ y = \frac{1}{4}(0) - 3 = 0 - 3 = -3 \] The point \( (0, 1.5) \) gives \( y = 1.5 \), which does not match. Thus, this point is not a solution to the equation. This statement is false.
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Statement C: (4, -1.5) is not a solution to the equation but is a point on the graph.
- Substitute \( x = 4 \) into the equation: \[ y = \frac{1}{4}(4) - 3 = 1 - 3 = -2 \] The point \( (4, -1.5) \) gives \( y = -1.5 \), which does not match. Therefore, it is not a solution.
- However, we check if \( (4, -1.5) \) can be on the graph. Since \( -1.5 \) does not equal \( -2 \), this point is also not on the graph. Hence, this statement is false.
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Statement D: (-1, -3.25) is a solution to the equation and is a point on the graph.
- Substitute \( x = -1 \) into the equation: \[ y = \frac{1}{4}(-1) - 3 = -0.25 - 3 = -3.25 \] The point \( (-1, -3.25) \) gives a matching \( y \)-value. Thus, this point is both a solution and is on the graph. Hence, this statement is true.
Since the only true statement is D, the answer is:
D. (-1, -3.25) is a solution to the equation and is a point on the graph.