Question

PLEASE HELP!!!

The graph shows the distance, y, that a car traveled in x hours:

What is the rate of change for the relationship represented in the graph?

1/35

1/34

34

35

Answer 1

the rate of change (the slope) is 35

Answer 2

35

Explanation:

This graph is really simple, you can infer the rate of change just by looking at it. As you can see, for every step it increments in the x-axis, it increments 35 in the y-axis. However, let's solve it step by step.

The rate of change that the points of a line show in their y-coordinates with respect to their x-coordinates is known as the slope of the line m. This means the relationship between how much change y with respect to how much change x, y can be expressed as follows:

`m=(y_2-y_1)/(x_2-x_1)`

In order to calculate the slope m, we just need two points. You can extract any of them, of course the best decision is to take integer numbers. Let's take the following points:

`P1=(x_1,y_1)=(0,0)\\P2=(x_2,y_2)=(4,140)`

Therefore, the rate of change for the relationship represented in the graph is:

`m=(140-0)/(4-0) =(140)/(4) =35`