To find the slope and the 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 equation:
\[ 4x - 3y = 12 \]
We want to solve for \(y\). First, isolate the term with \(y\):
\[ -3y = -4x + 12 \]
Next, divide every term by \(-3\):
\[ y = \frac{4}{3}x - 4 \]
Now that we have the equation 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 correct answer is:
B. The slope is \( \frac{4}{3} \), and the y-intercept is \((0, -4)\).
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