To identify the slope and the y-intercept of the equation \(4x - 3y = 12\), we can rewrite the equation in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the given equation:
\[ 4x - 3y = 12 \]
We can isolate \(y\):
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Subtract \(4x\) from both sides:
\[-3y = -4x + 12\]
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Divide by \(-3\):
\[y = \frac{4}{3}x - 4\]
From this, we can see that the slope \(m\) is \(\frac{4}{3}\), and the y-intercept \(b\) is \(-4\).
Thus, the slope is \(\frac{4}{3}\) and the y-intercept is \((0, -4)\).
So, the correct identification is:
The slope is \(\frac{4}{3}\), and the y-intercept is \((0, -4)\).
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