To determine which ordered pairs represent points on the graph of the equation \( y = -\frac{3}{4}x - \frac{1}{2} \), you can substitute the x-values of the ordered pairs into the equation to see if the resulting \( y \)-value matches the one given in the ordered pair.
Let's break down the equation \( y = -\frac{3}{4}x - \frac{1}{2} \):
- Pick an ordered pair and substitute \( x \) into the equation.
- Calculate \( y \) using the equation.
- Check if the calculated \( y \) from the equation matches the given \( y \) in the ordered pair.
Since you did not provide specific ordered pairs, I will demonstrate using a few examples:
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(0, -0.5): \[ y = -\frac{3}{4}(0) - \frac{1}{2} = -\frac{1}{2} \] This ordered pair is valid.
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(4, -3): \[ y = -\frac{3}{4}(4) - \frac{1}{2} = -3 - \frac{1}{2} = -3.5 \] This does not match.
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(-4, 2): \[ y = -\frac{3}{4}(-4) - \frac{1}{2} = 3 - \frac{1}{2} = 2.5 \] This does not match.
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(2, -2): \[ y = -\frac{3}{4}(2) - \frac{1}{2} = -\frac{3}{2} - \frac{1}{2} = -2 \] This pair is valid.
You can provide your own set of ordered pairs if they are specific, and I can help you determine which of them lie on the line represented by the equation.