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