Question

11.
Find the slope and y-intercept of the line.

18x + 4y = 112

Answer 1

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:

1. Subtract \(18x\) from both sides:

\[
4y = -18x + 112
\]

2. Divide every term by \(4\) to solve for \(y\):

\[
y = -\frac{18}{4}x + \frac{112}{4}
\]

3. 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 \(28\).