To find the slope and y-intercept of the line given by the equation \( 18x + 4y = 112 \), you need to rearrange the equation 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:
\[ 18x + 4y = 112 \]
Subtract \( 18x \) from both sides:
\[ 4y = -18x + 112 \]
Now, divide each term by \( 4 \) to solve for \( y \):
\[ y = -\frac{18}{4}x + \frac{112}{4} \]
Simplifying the coefficients:
\[ y = -\frac{9}{2}x + 28 \]
From this equation, we can see:
- The slope \( m \) is \( -\frac{9}{2} \).
- The y-intercept \( b \) is \( 28 \).
Thus, the slope is \( -\frac{9}{2} \) and the y-intercept is \( 28 \).