To find the slope and the y-intercept of the equation \( 4x - 3y = 12 \), we can rearrange the equation into the 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 \( y \):
- Move \( 4x \) to the other side:
\[ -3y = -4x + 12 \]
- Divide every term by -3:
\[ y = \frac{4}{3}x - 4 \]
From this equation, we can identify:
- The slope \( m = \frac{4}{3} \)
- The y-intercept \( b = -4 \), 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).