Question

Which linear function has the greatest y-intercept?
y = 6 x + 1
On a coordinate plane, a line goes through points (0, 2) and (5, 0).
On a coordinate plane, a line goes through points (1, 2) and (0, negative 3).
y = 3 x + 4

Answer 1

To find the linear function with the greatest y-intercept, we need to identify the y-intercepts of each given line:

1. **For the function:**
\( y = 6x + 1 \)
The y-intercept is \( 1 \) (this is the constant term).

2. **For the line through the points (0, 2) and (5, 0):**
The y-intercept is \( 2 \) (since this is the y-coordinate when \( x = 0 \)).

3. **For the line through the points (1, 2) and (0, -3):**
The y-intercept is \( -3 \) (since this is the y-coordinate when \( x = 0 \)).

4. **For the function:**
\( y = 3x + 4 \)
The y-intercept is \( 4 \) (the constant term).

Now we compare the y-intercepts:
- \( 1 \) from \( y = 6x + 1 \)
- \( 2 \) from the line through (0, 2) and (5, 0)
- \( -3 \) from the line through (1, 2) and (0, -3)
- \( 4 \) from \( y = 3x + 4 \)

The greatest y-intercept is \( 4 \) from the function \( y = 3x + 4 \).

Therefore, **the linear function with the greatest y-intercept is \( y = 3x + 4 \).**