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 math sentence with an equal sign.
• variable — A letter that stands for a number.
• rate — Two amounts compared, like miles for each hour.
• represent — Show it with a table, a graph, or an equation.
• define the variables — Say what each letter stands for.
• Constant — A number that stays the same.

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

A music streaming plan costs $8.99 per month. Let m = number of months and c = total cost. Which equation represents the relationship?

Check your answer

c = 8.99m

Each month costs $8.99, so the total cost is $8.99 multiplied by the number of months: c = 8.99m. Check: 3 months gives 8.99 × 3 = 26.97, so 3 months cost $26.97.

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.