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Algebra 1

1.3.2 Describing Relationships Using Words and Equations

Algebra 11.3.2 Describing Relationships Using Words and Equations

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Activity

Create a math story that describes how the two quantities in each table are related.

1.

Table A

Number of Laps, x x 0 1 2.5 6 9
Meters Run, y y 0 400 1,000 2,400 3,600

2.

Table B

Meters From Home, x x 0 75 128 319 396
Meters From School, y y 400 325 272 81 4

3.

Table C

Electricity Bills in Dollars, x x 85 124 309 816
Total Expenses in Dollars, y y 485 524 709 1,216

4.

Table D

Monthly Salary in Dollars, x x 872 998 1,015 2,110
Amount Deposited in Dollars, y y 472 598 615 1,710

For questions 5 - 8, match each table from 1 - 4 to an equation that represents the relationship.

5.

Equation 1: 400 + x = y 400 + x = y

6.

Equation 2: x 400 = y x 400 = y

7.

Equation 3: x + y = 400 x + y = 400

8.

Equation 4: 400 x = y 400 x = y

Are you ready for more?

Extending Your Thinking

Express every number between 1 and 20 at least one way using exactly four 4s and any operations. For example, 1 could be written as 4 4 + 4 4 4 4 + 4 4 .

Video: Describing Relationships

Watch the following video to learn more about describing relationships using words and equations, specifically looking at the base and height of different rectangles.

Self Check

Miles from Home, x 0 5 10
Miles from School, y 30 25 20

Using the table above, what is an equation that shows the relationship between miles from home and miles from school?

  1. y = 30 x
  2. y = 30 x
  3. y = 20 + x
  4. y = 30 + x

Additional Resources

Modeling Linear Equations

Given a real-world problem, model a linear equation to fit it using these steps:

Step 1 - Read the problem.

Step 2 - Identify the variables and known values. If needed, sketch a picture of the scenario.

Step 3 - Write a sentence or create a table using the relationship among the values.

Step 4 - Translate the sentence or table into an equation

Let’s look at an example. Using the steps above, we can model a linear equation to solve a real-world application.

Example

Cell phone Company A charges a monthly service fee of $34 plus $0.05/minute talk time.

Step 1 - Read the problem.
Cell phone Company A charges a monthly service fee of $34 plus $0.05/minute talk time.

Step 2 - Identify the variables and known values. If needed, sketch a picture of the scenario.
t t : total cost (in dollars)
m m : number of minutes

Step 3 - Write a sentence or create a table using the relationship among the values.

Minutes Talked in One Month 0 1 2 3 100
Total for One Month (Dollars) 34 34.05 34.10 34.15 39
Company A:

Company A: The total cost, t t , equals the fee, 34, plus 0.05 per minute, 0.05 m 0.05 m .

Step 4 - Translate the sentence or table into an equation.
t = 34 + 0.05 m t = 34 + 0.05 m

Try it

Try It: Modeling Linear Equations

Cell phone Company B charges a monthly service fee of $40 plus $0.04/min talk-time. Write an equation to describe the relationship between the number of minutes and the total cost.

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