Question

Find the slope and y-intercept of the line.

18x + 4y = 112

Answer 1

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.

1. Start with the original equation:

\[
18x + 4y = 112
\]

2. Solve for \(y\) by isolating it on one side of the equation. First, subtract \(18x\) from both sides:

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

3. Next, divide every term by \(4\) to solve for \(y\):

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

4. 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 \(28\).