To find the slope and the y-intercept of the equation \(4x - 3y = 12\), we can rearrange it into the slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \((0, b)\) is the y-intercept.
Starting with the equation:
\[ 4x - 3y = 12 \]
- Subtract \(4x\) from both sides:
\[ -3y = -4x + 12 \]
- Divide each term by \(-3\):
\[ y = \frac{4}{3}x - 4 \]
From this form, we can identify:
- The slope \(m = \frac{4}{3}\)
- The y-intercept \(b = -4\), which means the y-intercept in coordinate form is \((0, -4)\).
Thus, the correct answer is:
The slope is \( \frac{4}{3} \), and the y-intercept is \((0, -4)\).
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