To find the slope and y-intercept of the line given by the equation \(18x + 4y = 112\), 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.
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Start with the original equation:
\[ 18x + 4y = 112 \]
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Solve for \(y\) by isolating it on one side of the equation. First, subtract \(18x\) from both sides:
\[ 4y = -18x + 112 \]
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Next, divide every term by \(4\) to solve for \(y\):
\[ y = -\frac{18}{4}x + \frac{112}{4} \]
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Simplify the fractions:
\[ y = -\frac{9}{2}x + 28 \]
From the equation \(y = -\frac{9}{2}x + 28\), we can identify the slope and y-intercept:
- Slope (\(m\)): \(-\frac{9}{2}\)
- Y-intercept (\(b\)): \(28\)
Thus, the slope is \(-\frac{9}{2}\) and the y-intercept is \(28\).