To find the slope and the y-intercept of the equation \(4x - 3y = 12\), we can rewrite it in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the equation:
\[ 4x - 3y = 12 \]
We can isolate \(y\):
\[ -3y = -4x + 12 \]
Dividing each term by -3:
\[ y = \frac{4}{3}x - 4 \]
Now we can see that the slope \(m\) is \(\frac{4}{3}\) and the y-intercept \(b\) is \(-4\).
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).
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