To match a graph with the linear equation \(-2x + 3y = -6\), we first need to rearrange it into slope-intercept form (y = mx + b), which will make it easier to identify the line's characteristics such as slope and y-intercept.
Starting with the equation: \[ -2x + 3y = -6 \] we can solve for \(y\):
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Add \(2x\) to both sides: \[ 3y = 2x - 6 \]
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Divide every term by \(3\): \[ y = \frac{2}{3}x - 2 \]
Now, we have the equation in slope-intercept form \(y = \frac{2}{3}x - 2\).
From this, we can identify:
- The slope \(m\) is \(\frac{2}{3}\).
- The y-intercept is \(-2\).
This means the line crosses the y-axis at the point \((0, -2)\) and rises 2 units for every 3 units it moves to the right.
To match the graph:
- Look for a line that crosses the y-axis at \(-2\).
- The line should have a positive slope, indicating it rises from left to right.
If you have specific graph options, you can apply this information to determine which graph corresponds to the equation \(-2x + 3y = -6\).
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