Question

Find the slope and y-intercept of the line.

14x + 4y = 24


; mc005-6.jpg


14; 24


; 6


; 6

Answer 1

To find the slope and y-intercept of the line given by the equation \( 14x + 4y = 24 \), we need to rewrite it in the 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:
\[
14x + 4y = 24
\]

2. Isolate \( y \) by subtracting \( 14x \) from both sides:
\[
4y = -14x + 24
\]

3. Now, divide every term by \( 4 \) to solve for \( y \):
\[
y = -\frac{14}{4}x + \frac{24}{4}
\]

4. Simplify the fractions:
\[
y = -\frac{7}{2}x + 6
\]

Now, we can identify the slope and y-intercept:
- The slope (\( m \)) is \( -\frac{7}{2} \).
- The y-intercept (\( b \)) is \( 6 \).

In summary:
- **Slope**: \( -\frac{7}{2} \)
- **Y-intercept**: \( 6 \)