To convert the equation from standard form \(4x + 3y = 12\) to slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, follow these steps:
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Isolate \(y\): Start by moving the \(4x\) term to the right side of the equation. \[ 3y = -4x + 12 \]
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Solve for \(y\): Divide every term by \(3\) to solve for \(y\). \[ y = -\frac{4}{3}x + 4 \]
Now the equation is in slope-intercept form:
\[ y = -\frac{4}{3}x + 4 \]
Identifying the slope and y-intercept:
- Slope (\(m\)): \(-\frac{4}{3}\)
- Y-intercept (\(b\)): \(4\)
Thus, in slope-intercept form, the slope is \(-\frac{4}{3}\) and the y-intercept is \(4\).
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