To find the slope and y-intercept of the line represented by the equation \(18x + 4y = 112\), we first need to 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 original equation:
\[18x + 4y = 112\]
we can isolate \(y\) by following these steps:
- Subtract \(18x\) from both sides:
\[ 4y = -18x + 112 \]
- Divide every term by \(4\) to solve for \(y\):
\[ y = -\frac{18}{4}x + \frac{112}{4} \]
- Simplify:
\[ y = -\frac{9}{2}x + 28 \]
Now we can identify the slope and y-intercept:
- The slope \(m\) is \(-\frac{9}{2}\).
- The y-intercept \(b\) is \(28\).
Thus, the slope of the line is \(-\frac{9}{2}\) and the y-intercept is \(28\).