Lesson 3: Write Equations to Represent Relationships Between Two Variables6.AT.11

I can…

I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.

Key words

• equation — A mathematical sentence with an equals sign that shows two amounts are the same.
• variable — A letter that represents a quantity that can change, or vary.
• rate — A fixed amount of one quantity for every one unit of the other quantity.
• represent — To show a relationship using a tool such as a table, a graph, or an equation.
• define the variables — To state exactly what quantity each letter in an equation stands for.

Steps

1. The quantities are the number of months of membership and the total cost. The total cost depends on the number of months.
2. In the table, each month adds $24.95: 1 month is $24.95, 2 months are $49.90, 3 months are $74.85.
3. The pattern in words: the total cost is $24.95 times the number of months.
4. Define the variables — let m = number of months and c = total cost in dollars — and write the equation: c = 24.95m.
5. Now ANY number of months works: for 10 months, c = 24.95 × 10 = 249.50.

Try it

Recreation World charges $24.95 per month. Let m = number of months and c = total cost. Which equation represents the relationship?

Check your answer

c = 24.95m

Each month costs $24.95, so the total cost is $24.95 multiplied by the number of months: c = 24.95m. Check: 2 months gives 24.95 × 2 = 49.90, which matches the table.

Sentence starter

I know ___ because ___.

Goal: I can define the variables in my equation and explain what each part represents using the words equation, variable, and rate.