To determine which ordered pairs represent points on the graph of the equation \(-3x + 4y = -6\), we can substitute the \(x\) and \(y\) values from the ordered pairs into the equation and see if the equation holds true.
Let's rewrite the equation in a more manageable form to solve for \(y\):
\[ 4y = 3x - 6 \]
\[ y = \frac{3}{4}x - \frac{3}{2} \]
Now, consider various ordered pairs \((x, y)\) and substitute each into the equation to check if they satisfy it.
Here are a few examples of ordered pairs to evaluate:
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\((-2, 0)\): \[ -3(-2) + 4(0) = 6 + 0 = 6 \quad \text{(not equal to -6)} \]
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\((0, -1.5)\): \[ -3(0) + 4(-1.5) = 0 - 6 = -6 \quad \text{(equals -6)} \]
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\((2, 0)\): \[ -3(2) + 4(0) = -6 + 0 = -6 \quad \text{(equals -6)} \]
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\((0, -2)\): \[ -3(0) + 4(-2) = 0 - 8 = -8 \quad \text{(not equal to -6)} \]
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\((4, 6)\): \[ -3(4) + 4(6) = -12 + 24 = 12 \quad \text{(not equal to -6)} \]
After evaluating a number of pairs, you can continue testing potential ordered pairs in this way until you find all pairs that satisfy the equation.
Feel free to provide a specific list of points if you need further assistance checking them!