To identify the slope and the y-intercept of the equation \(4x - 3y = 12\), we can rearrange it into slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the original equation:
\[ 4x - 3y = 12 \]
We can isolate \(y\):
- Subtract \(4x\) from both sides:
\[ -3y = -4x + 12 \]
- Divide every term by \(-3\) to solve for \(y\):
\[ y = \frac{4}{3}x - 4 \]
Now, we can identify the slope and the y-intercept:
- The slope \(m\) is \(\frac{4}{3}\).
- The y-intercept \(b\) is \(-4\).
Thus, the slope is \(\frac{4}{3}\) and the y-intercept is \(-4\).
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