To identify the slope and y-intercept of the equation \( 4x - 3y = 12 \), we can rewrite the equation in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the original equation:
- Rearrange the equation to solve for \( y \): \[ -3y = -4x + 12 \] \[ y = \frac{4}{3}x - 4 \]
Now we can see that the equation is in the form \( y = mx + b \).
- The slope \( m \) is \( \frac{4}{3} \).
- The y-intercept \( b \) is \(-4\), which corresponds to the point \( (0, -4) \).
Thus, the slope is \( \frac{4}{3} \), and the y-intercept is \( (0, -4) \).
The correct response is: The slope is \( \frac{4}{3} \), and the y-intercept is \( (0, -4) \).