Question

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

(1 point)
Responses

3x+8y=24
3 x plus 8 y is equal to 24

y=15x+5
y is equal to 15 x plus 5

y=4x+7
y is equal to 4 x plus 7

x+6y=36

Answer 1

To find the linear function with the greatest y-intercept, we need to express each given equation in the slope-intercept form (y = mx + b), where b is the y-intercept.

1. For the equation **3x + 8y = 24**:
\[
8y = -3x + 24 \\
y = -\frac{3}{8}x + 3 \quad \text{(y-intercept is 3)}
\]

2. For the equation **y = 15x + 5**:
- The y-intercept is 5.

3. For the equation **y = 4x + 7**:
- The y-intercept is 7.

4. For the equation **x + 6y = 36**:
\[
6y = -x + 36 \\
y = -\frac{1}{6}x + 6 \quad \text{(y-intercept is 6)}
\]

Now, let's summarize the y-intercepts:
- From \(3x + 8y = 24\), y-intercept = 3
- From \(y = 15x + 5\), y-intercept = 5
- From \(y = 4x + 7\), y-intercept = 7
- From \(x + 6y = 36\), y-intercept = 6

The greatest y-intercept is **7** from the equation **y = 4x + 7**.

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