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Algebra 1

2.2.2 Writing Systems of Equations from Tables

Algebra 12.2.2 Writing Systems of Equations from Tables

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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?

1.

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

2.

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

3.

For Option A, identify the yy-intercept (where x=0x=0).

4.

For Option A, identify the slope between any two points.

5.

For Option A, write an equation of the line in slope-intercept form.

6.

For Option B, identify the yy-intercept (where x=0x=0).

7.

For Option B, identify the slope between any two points.

8.

For Option B, write an equation of the line in slope-intercept form.

9.

Write the system of equations.

10.

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.

11.

What is the point of intersection of the two lines?

12.

Talk with your partner. What does this intersection mean in the context of the problem?

13.

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.

Self Check

A streaming service offers two options for subscription plans. Option A charges $10.99 a month plus $2 per movie. Option B charges $5.99 a month plus $3 per movie. The table below describes this. Which of the following systems of equations represents the two options for one month?

x (Number of movies 0 1 2 3
Option A 10.99 12.99 14.99 16.99
Option B 5.99 8.99 11.99 14.99
  1. y = 2 x + 10.99

    y = 3 x + 5.99


  2. y = 3 x + 10.99

    y = 2 x + 5.99


  3. y = 2 x 10.99

    y = 3 x 5.99


  4. y = 10.99 x + 2

    y = 5.99 x + 3

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 yy-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.

A table shows time (t) in seconds: 0, 1, 2, 3. Corresponding distances (D(t)) are 250, 333, 416, and 499 meters. Arrows indicate each second covers 83 meters.

Step 1 - Find the yy-intercept.

Notice that when t=0,D(t)=250t=0,D(t)=250. This is the yy-intercept.

Step 2 - Find the slope.

To find the slope, find the change of yy over the change of x:m=831=83x:m=831=83.

Step 3 - Write the equation in slope-intercept form.

y=mx+by=mx+b, where mm is the slope and bb is the yy-intercept.

y=83x+250y=83x+250

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, xx months since the measurements began. Write a linear function, H(x)H(x), where xx is the number of months since the start of the experiment.

xx 0 2 4 8 12
H(x)H(x) 12.5 13.5 14.5 16.5 18.5

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