To identify the slope and the y-intercept of the equation \(4x - 3y = 12\), we first need to rearrange it into the slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the equation:
\[ 4x - 3y = 12 \]
We can isolate \(y\):
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Subtract \(4x\) from both sides:
\[-3y = -4x + 12\]
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Now, divide each term by \(-3\):
\[y = \frac{4}{3}x - 4\]
From this equation, we can see that:
- The slope \(m\) is \(\frac{4}{3}\).
- The y-intercept \(b\) is \(-4\), which corresponds to the point \((0, -4)\).
Thus, the correct response is:
The slope is \( \frac{4}{3} \), and the y-intercept is \((0, -4)\).