To determine which graph matches the linear equation \(-2x + 3y = -6\), you'll want to rewrite the equation in slope-intercept form, which is \(y = mx + b\).
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Start with the equation: \[-2x + 3y = -6\]
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Add \(2x\) to both sides: \[3y = 2x - 6\]
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Divide each term by \(3\): \[y = \frac{2}{3}x - 2\]
From this form, we can determine:
- The slope (\(m\)) is \(\frac{2}{3}\).
- The y-intercept (\(b\)) is \(-2\).
Now, to find the graph that matches this equation, look for the following characteristics:
- The line should slope upwards from left to right due to a positive slope of \(\frac{2}{3}\).
- The line should cross the y-axis at \(-2\).
If you can provide graphs to choose from or describe them, I can help identify which one matches this equation.
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