Question

Select the linear function that has the greatest y-intercept.

A. y=4x+7
B. y=15x+5
C. 3x+8y=24
D. x+6y=36

Answer 1

To find the linear function with the greatest y-intercept, we need to inspect the y-intercepts of each equation.

1. **A. \( y = 4x + 7 \)**: The y-intercept is \( 7 \).

2. **B. \( y = 15x + 5 \)**: The y-intercept is \( 5 \).

3. **C. \( 3x + 8y = 24 \)**: We need to rewrite this in slope-intercept form (y = mx + b).
- Rearranging gives us \( 8y = -3x + 24 \).
- Dividing by 8 gives \( y = -\frac{3}{8}x + 3 \). The y-intercept is \( 3 \).

4. **D. \( x + 6y = 36 \)**: We also need to rewrite this in slope-intercept form.
- Rearranging gives \( 6y = -x + 36 \).
- Dividing by 6 gives \( y = -\frac{1}{6}x + 6 \). The y-intercept is \( 6 \).

Now summarizing the y-intercepts we found:
- A: \( 7 \)
- B: \( 5 \)
- C: \( 3 \)
- D: \( 6 \)

The greatest y-intercept is **7** from option **A**.

Thus, the linear function with the greatest y-intercept is:
**A. \( y = 4x + 7 \)**.