To determine which ordered pairs represent points on the graph of the equation \( \frac{2}{3}y = -\frac{1}{2}x \), we can rearrange the equation into a more familiar form, if needed, or simply plug in the \( x \) and \( y \) values from the provided ordered pairs to check if they satisfy the equation.
First, let's rearrange the equation for easier calculation:
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Multiply both sides by 6 to eliminate the fractions: \[ 6 \left(\frac{2}{3}y\right) = 6 \left(-\frac{1}{2}x\right) \] This simplifies to: \[ 4y = -3x \]
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Now, let's express \( y \): \[ y = -\frac{3}{4}x \]
Now, if you have specific ordered pairs (like (x, y) points), substitute the \( x \) values into this equation to check if the corresponding \( y \) values match.
For example, if we check these pairs:
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\( (0, 0) \):
- Substitute: \( y = -\frac{3}{4}(0) = 0 \) → Point is (0, 0) on the graph.
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\( (4, -3) \):
- Substitute: \( y = -\frac{3}{4}(4) = -3 \) → Point is (4, -3) on the graph.
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\( (8, -6) \):
- Substitute: \( y = -\frac{3}{4}(8) = -6 \) → Point is (8, -6) on the graph.
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\( (2, 1) \):
- Substitute: \( y = -\frac{3}{4}(2) = -1.5 \) → Point is not (2, 1) on the graph.
Continue this process for any pairs you have in mind.
Please list the ordered pairs that you're checking, and I can help verify which ones are on the graph of the equation given!