Question

Select the linear function that has the sleepest slope.

A. y = 4x + 7
B. -x + 6y = 36
C. y = -10x + 5
D. 3x + 8y = 24

Answer 1

To determine which linear function has the steepest slope, we need to identify the slope of each equation. Here's how to do that:

A. **y = 4x + 7**
- The slope (m) is 4.

B. **-x + 6y = 36**
- Rearranging to slope-intercept form (y = mx + b):
\[
6y = x + 36 \implies y = \frac{1}{6}x + 6
\]
- The slope (m) is \(\frac{1}{6}\).

C. **y = -10x + 5**
- The slope (m) is -10.

D. **3x + 8y = 24**
- Rearranging to slope-intercept form (y = mx + b):
\[
8y = -3x + 24 \implies y = -\frac{3}{8}x + 3
\]
- The slope (m) is -\(\frac{3}{8}\).

Now we compare the slopes:
- A: slope = 4
- B: slope = \(\frac{1}{6}\)
- C: slope = -10
- D: slope = -\(\frac{3}{8}\)

The steepest slope refers to the largest absolute value of the slope. The absolute values of the slopes are:
- A: |4| = 4
- B: |\(\frac{1}{6}\)| = \(\frac{1}{6}\)
- C: |-10| = 10
- D: |-\(\frac{3}{8}\)| = \(\frac{3}{8}\)

The largest absolute value is from option C, where the slope is -10. Therefore, it has the steepest slope.

**The function with the steepest slope is C. y = -10x + 5.**