To determine the slope and the y-intercept of the equation \(4x - 3y = 12\), we can rearrange it into slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
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Start with the equation: \[ 4x - 3y = 12 \]
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Solve for \(y\): \[ -3y = -4x + 12 \] \[ y = \frac{4}{3}x - 4 \]
From this form, we can see that:
- The slope \(m\) is \(\frac{4}{3}\).
- The y-intercept \(b\) is \(-4\), which means the y-intercept point is \((0, -4)\).
Therefore, the correct response is:
- The slope is \(\frac{4}{3}\), and the y-intercept is \((0, -4)\).
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