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Data regarding fuel efficiency of an 18-wheel truck were collected. The graph shows the correlation between the average speed above 40 miles per hour (in miles per hour) and the money spent on gas (in dollars):

image of a scatter plot with Average Speed on the x axis and Money Spent on Fuel on the y axis with points 1 comma 2, 3 comma 2 and one half, 5 comma 5, 7 comma 7, 9 comma 10, 11 comma 15, and 12 comma 17

Estimate the average rate of change from x = 5 to x = 9.

4
−4
0.8
1.25

When we talk about the rate of change, we refer to the ratio of each variable change, how much change the Average Speed with respect to Money Spend, this is geometrically referring to a slope, which is the ratio of change of a linear relation between two variables.

So, the points to calculate the ratio are (5;5) and (9;10), because the problem is asking from x = 5 to x = 9:

[tex]m=\frac{10-5}{9-5}=\frac{5}{4}=1.25 \frac{money}{speed}[/tex]

This means that the ratio is 1.25 units of money spent by each unit of average speed.

crazymonkey88 crazymonkey88 · Answer 2 · 2021-05-07T20:28:34+02:00

Answer:

For those of you here for the rate of change between x=15 to x=19 with the same graph as the one saved below:

Your answer will be −3.25!

For those of you who are here for either the question posted or one that is similar in nature:

You can use the information below to help you!

Step-by-step explanation:

What is the Rate of Change?:

A rate of change defines how one quantity changes in relation to another quantity. The rate of change can be either positive or negative. Since the slope of a line is the ratio of vertical and horizontal change between two points on the plane or a line, then the slope equals the ratio of the rise and the run.

Where,

Rise is the vertical change between two points

Run is the horizontal change between two points

Standard Formula:

The standard form for the rate of change of slope, m is given by

Rate of change = Rise/ Run

= Δy / Δx

Therefore, the rate of change of slope =(y2 – y1) / (x2 – x1)

Where

Δ represents the rate of change

(x1, x2) is the X coordinates

(y1, y2) is the Y coordinates

For further assistance: visit BYJU'S rate of change calculator.