Question

What are the slope and the y-intercept of the linear function that is represented by the graph?

On a coordinate plane, a line goes through points (0, 3) and (4, 0).
The slope is Negative four-thirds, and the y-intercept is 3.
The slope is Negative four-thirds, and the y-intercept is 4.
The slope is Negative three-fourths, and the y-intercept is 3.
The slope is Negative three-fourths, and the y-intercept is 4.

Answer 1

To find the slope (m) and y-intercept (b) of the linear function that passes through the points (0, 3) and (4, 0):

1. **Identify the points**: The points you have are:
- Point 1: (0, 3) (This is the y-intercept, so b = 3)
- Point 2: (4, 0)

2. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the coordinates of the points:
- \(y_1 = 3\)
- \(y_2 = 0\)
- \(x_1 = 0\)
- \(x_2 = 4\)

Plugging these values in:
\[
m = \frac{0 - 3}{4 - 0} = \frac{-3}{4}
\]

Thus, the slope is \(-\frac{3}{4}\), and the y-intercept is 3.

The correct choice is: **The slope is Negative three-fourths, and the y-intercept is 3.**