Activity
This summer, the Farmer’s Almanac is calling for very high temperatures in central Texas. Mr. and Mrs. Flores were talking about ways to keep their four children cool during the summer and also ways that the family could have fun together. They decided that this summer they would purchase a family membership to the community pool.
Mrs. Flores called the community pool to find out different membership plans for a family of six. The receptionist at the community center told her that there are two options. Option A is to pay $100 for the summer and $20 per visit. The second option, Option B, is to pay $250 for the summer and $5 per visit.
At dinner, the Flores family talked about how many times a week they think they will visit the pool and how many times total in the summer they will visit.
How can the Flores family decide which option to choose? Which option do you think they will pick and why?
Make a table of values for Option A for 0–10 visits.
Option A:
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Compare your answer:
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
100 | 120 | 140 | 160 | 180 | 200 | 220 | 240 | 260 | 280 | 300 |
Make a table of values for Option B for 0–10 visits.
Option B:
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Compare your answer:
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
250 |
255 |
260 |
265 |
270 |
275 |
280 |
285 |
290 |
295 |
300 |
For Option A, identify the -intercept (where ).
100
For Option A, identify the slope between any two points.
20
For Option A, write an equation of the line in slope-intercept form.
Compare your answer:
For Option B, identify the -intercept (where ).
250
For Option B, identify the slope between any two points.
5
For Option B, write an equation of the line in slope-intercept form.
Compare your answer:
Write the system of equations.
Compare your answer:
Answer:
Use the graphing tool or technology outside the course. Graph your system of equations from question 9 that represents this scenario using the Desmos tool below.
Compare your answer:
What is the point of intersection of the two lines?
Compare your answer:
Talk with your partner. What does this intersection mean in the context of the problem?
Compare your answer:
At 10 visits, the cost is the same at $300.
Write a paragraph to describe when Option A is better and when Option B is better. Share your paragraph with your partner. Read each other’s paragraphs and then discuss if you agree or disagree.
Compare your answer:
Your answer may vary, but here is a sample. The two options cost the same at 10 visits. Since Option A is less money up front, Option A will be less expensive until the 10th visit. After 10 visits, however, Option B is less expensive.
Self Check
Additional Resources
Representing a Linear Function in Tabular Form
A system of equations is two or more equations. Often, each equation in a system of equations represents a situation. Like other equations, the equations that make up the system can be represented by a table. When writing any equation from a table into slope-intercept form, two things are needed: a slope and point, often the -intercept.
Example
Suppose a maglev train travels a long distance, and maintains a constant speed of 83 meters per second for a period of time once it is 250 meters from the station. Here is a table that shows this constant speed.
Step 1 - Find the -intercept.
Notice that when . This is the -intercept.
Step 2 - Find the slope.
To find the slope, find the change of over the change of .
Step 3 - Write the equation in slope-intercept form.
, where is the slope and is the -intercept.
Try it
Try It: Representing a Linear Function in Tabular Form
A new plant food was introduced to a young tree to test its effect on the height of the tree. The table shows the height of the tree, in feet, months since the measurements began. Write a linear function, , where is the number of months since the start of the experiment.
0 | 2 | 4 | 8 | 12 | |
12.5 | 13.5 | 14.5 | 16.5 | 18.5 |
Compare your answer:
Here is how to write an equation from the table.
Step 1 - Find the -intercept.
Notice that when , . This is the -intercept.
Step 2 - Find the slope.
To find the slope, find the change of over the change of : .
Step 3 - Write the equation in slope-intercept form.
, where is the slope and is the -intercept.