To find the slope and the y-intercept of the equation \(4x - 3y = 12\), we first need to rewrite it in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the equation:
\[ 4x - 3y = 12 \]
Now, solve for \(y\):
- Subtract \(4x\) from both sides:
\[ -3y = -4x + 12 \]
- Divide by \(-3\):
\[ y = \frac{4}{3}x - 4 \]
From this form, we can see that:
- The slope \(m\) is \(\frac{4}{3}\).
- The y-intercept \(b\) is \(-4\).
Thus, the y-intercept in coordinate form is (0, -4).
The correct response is:
The slope is \( \frac{4}{3} \), and the y-intercept is (0, −4).