To graph the equation \(2x - 3y = -6\), we can rearrange it into slope-intercept form (\(y = mx + b\)).
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Start with the original equation:
\[ 2x - 3y = -6 \]
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Solve for \(y\):
\[ -3y = -2x - 6 \] \[ y = \frac{2}{3}x + 2 \]
Now, we can identify the slope (\(m\)) and the y-intercept (\(b\)):
- The slope \(m = \frac{2}{3}\)
- The y-intercept \(b = 2\) (the point where the line crosses the y-axis)
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To graph the line:
- Start at the y-intercept (0, 2) on the graph.
- From that point, use the slope to find another point. Since the slope is \(\frac{2}{3}\), go up 2 units and to the right 3 units. This brings you to the point (3, 4).
- You can also find a third point by going in the opposite direction: from (0, 2), go down 2 units and to the left 3 units, which brings you to the point (-3, 0).
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Plot the points (0, 2), (3, 4), and (-3, 0) on a coordinate plane.
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Draw a straight line through the points.
This will give you the graph of the equation \(2x - 3y = -6\).