Question

Select the linear function that has the steepest slope.

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

Answer 1

To find the linear function with the steepest slope, we need to determine the slope of each function.

1. **For A: \(3x + 8y = 24\)**, we can rearrange it into slope-intercept form \(y = mx + b\):

\[
8y = -3x + 24 \quad \Rightarrow \quad y = -\frac{3}{8}x + 3
\]

The slope \(m\) here is \(-\frac{3}{8}\).

2. **For B: \(y = 4x + 7\)**, the slope is directly visible:

The slope \(m\) is \(4\).

3. **For C: \(y = -10x + 5\)**, the slope is also directly visible:

The slope \(m\) is \(-10\).

4. **For D: \(-x + 6y = 36\)**, we rearrange it into slope-intercept form:

\[
6y = x + 36 \quad \Rightarrow \quad y = \frac{1}{6}x + 6
\]

The slope \(m\) here is \(\frac{1}{6}\).

Now, summarizing the slopes we found:
- A: \(-\frac{3}{8}\)
- B: \(4\)
- C: \(-10\)
- D: \(\frac{1}{6}\)

The steepest slope is the largest in absolute value but also positive. Among all the slopes, the largest is:

- B: \(4\)

Thus, the linear function with the steepest slope is **B: \(y = 4x + 7\)**.