To determine which equations represent the given points, we will check each equation by substituting the x and y values of the dots (0, 5), (3, 3), and (6, 1) into the equations.
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\(2x + 3y = 15\):
- For Dot 1 (0, 5): \(2(0) + 3(5) = 15\) → \(15 = 15\) (True)
- For Dot 2 (3, 3): \(2(3) + 3(3) = 15\) → \(6 + 9 = 15\) → \(15 = 15\) (True)
- For Dot 3 (6, 1): \(2(6) + 3(1) = 15\) → \(12 + 3 = 15\) → \(15 = 15\) (True)
- This equation is valid for all points.
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\(y = -\frac{2}{3}x + 5\):
- For Dot 1 (0, 5): \(y = -\frac{2}{3}(0) + 5\) → \(y = 5\) (True)
- For Dot 2 (3, 3): \(y = -\frac{2}{3}(3) + 5\) → \(y = -2 + 5 = 3\) (True)
- For Dot 3 (6, 1): \(y = -\frac{2}{3}(6) + 5\) → \(y = -4 + 5 = 1\) (True)
- This equation is valid for all points.
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\(y = 5x + 8\):
- For Dot 1 (0, 5): \(y = 5(0) + 8\) → \(y = 8\) (False)
- This equation is not valid for all points.
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\(-3x + 2y = 5\):
- For Dot 1 (0, 5): \(-3(0) + 2(5) = 5\) → \(10 = 5\) (False)
- This equation is not valid for all points.
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\(y = 5x - 2\):
- For Dot 1 (0, 5): \(y = 5(0) - 2\) → \(y = -2\) (False)
- This equation is not valid for all points.
Conclusion:
The equations that could represent the given graph with the points (0, 5), (3, 3), and (6, 1) are:
- \(2x + 3y = 15\)
- \(y = -\frac{2}{3}x + 5\)