Graphing+Linear+Functions-Target+F-Rate+It-Guided+Learning

Target F: Identify and compare rates of change.

 * [[image:Discuss this.png width="173" height="97"]] || An announcer on a radio broadcast expresses concern about a baseball player not hitting a homerun in his last 13 at bats during the playoffs. During the regular season the player hit a homerun in every nine at bats on average. For the playoffs the hitter had hit 3 homeruns in his first 14 at bats. Explain whether the radio broadcaster is correct in his concern about the homerun rate. ||

Recall, when finding slope of a line that passes through two points, use the formula:

math \LARGE \frac{y_{2}-y_{1}}{x_{2}-x_{1_{}}} math When finding slope from a graph, select two points the line passes through and find the rise over run:

math \LARGE \frac{rise}{run} math Rate of change is represented as the change in y over the change in x. It is a comparison of a change in one quantity over a change in another. For example, miles per hour is a rate of change.

Comparing rates of change can be used to determine cost effectiveness. For example, when looking at dog care, comparing the rates of change can help decide which company charges less. Look at the table below. The rate of change with respect to this table can be interpreted as the cost per dog walked. Find the rate of change for each company to determine which one offers the better the deal.
 * Comparing Rates of Change - From Tables**

To find the rate of change for the company Doggy Dash, select two (x, y) pairs and find the slope: (3, 9) and (6, 18).

math \Large \frac{total \ cost}{dogs \ walked}=\frac{18-9}{6-3}=\frac{9}{3}=\frac{3}{1} math So the rate of change for Doggy Dash would be $3 per dog walked. When describing rate of change, labels are important. It is necessary to know the two quantities that are being compared. For this problem, the two quantities are money and the number of dogs walked.

Do the same to find the rate of change for the company Doggy Care

math \Large \frac{total \ cost}{dogs \ walked}=\frac{35-21}{10-6}=\frac{14}{4}=\frac{7}{2} math

The rate of change for Doggy Care would be $3.50 per dog walked. After comparing the rates of change between the two companies, it becomes clear that the better company, in terms of cost, would be Doggy Dash because they charge less to walk a dog than Doggy Care. The following graphs represent two different cable companies and what they charge monthly for cable. The red line represents Cabletown and the blue line represents Crazy Cable.
 * Comparing Rates of Change - From Graphs**



The rate of change for Cabletown (red) is $40 per month. To find this, identify the rise over run for the red line. Make sure to pay attention to the intervals along each axis. Although the rise along the red line is 1 unit, each interval increases by 40 along the y-axis.

Using the same reasoning as above, the rate of change for Crazy Cable (blue) is $120 per month.

The graph can be used to compare the rate of change for each cable company. It can also be used to identify additional information. For example, the y-intercept of each line represents the initial fee for each cable company. The installation fee for Cabletown is $160, because the y-intercept of the red line is located at (0, 160). The installation fee for Crazy Cable is $40, because the y-intercept of the blue line is at (0, 40).

**Quick Check** Kinder Brook, Sycamore Valley, and Clifford Creek offer unlimited passes for golf. The table shows the cost for Kinder Brook and Clifford Creek golf courses. The graph shows the cost for Sycamore Valley golf course. Find the rates of change per month between the three golf courses and answer the questions below.



a) How much more does Sycamore Valley charge over Kinderbrook per month? b) How much does Clifford Creek charge per month for an unlimited pass? c) Which golf course offers the best monthly deal for a membership? Quick Check Solutions - Graphing Linear Functions - Target F Identify and Compare Rates of Change