Question

The graph of a linear function is shown on the coordinate grid below.

What are the slope and y-intercept of the linear function shown in the grid?

A) Slope = –0.4, y-intercept = –5
B) Slope = 2.5, y-intercept = –5
C) Slope = –2.5, y-intercept = 2
D) Slope = 0.4, y-intercept = 2

Answer 1

B) Slope = 2.5, y-intercept = –5

Explanation:

Given the following points on the grid, (-1.5, -8.75) and (3.5, 3.75), the slope can be calculated as follows using the formula,
`m = (y_2 - y_1)/(x_2 - x_1)`

Let,

`(-1.5, -8.75) = (x_1, y_1)`

`(3.5, 3.75) = (x_2, y_2)`

`m = (3.75 -(-8.75))/(3.5 -(-1.5))`

`m = (3.75 + 8.75)/(3.5 + 1.5)`

`m = (12.5)/(5)`

`m = 2.5`

Slope = 2.5.

The y-intercept is the point at which the line intercepts the y-axis. On the graph, the line intercepts the y-axis at y = -5. Therefore, the y-intercept = -5.