To find the slope and the y-intercept of the equation \(4x - 3y = 12\), we can rearrange it into the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the original equation: \[ 4x - 3y = 12 \]
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Subtract \(4x\) from both sides: \[ -3y = -4x + 12 \]
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Now, divide each term by \(-3\) to solve for \(y\): \[ y = \frac{4}{3}x - 4 \]
From this equation, we can identify:
- The slope \(m = \frac{4}{3}\)
- The y-intercept \(b = -4\), which corresponds to the point \((0, -4)\).
Thus, the correct answer is: The slope is \(\frac{4}{3}\), and the y-intercept is (0, −4).