Question

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?

55
54
fraction 1 over 54
fraction 1 over 55

Answer 1

Answer: 55 miles per hour

Explanation:

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

The rate of change of a function is given by :-

`k=\frac{\text{Change in y}}{\text{Change in x}}`

When we look in the graph , we observe that the graph is passing through two points (0,0) and (1,55).

Now, the rate of change for the relationship represented in the graph will be :_

`k=(55-0)/(1-0)=55`

Hence, the rate of change for the relationship represented in the graph is 55 miles per hour.

Answer 2

Here, You need to calculate the slope of the graph by taking any two random points, as follows:
(x₁,y₁) = (0,0) & (x₂,y₂) = (1,55)

Now, we know,
y₂-y₁ = m(x₂-x₁)
55-0 = m(1-0)
m = 55/1
m = 55

Here m represents the slope of graph which is nothing but rate of change of distance.

In short, option A will be your answer.

Hope this helps!