Lesson 9.3Equations from Situations
Start hereWords, worked example, and sentence starters
Learning target I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| equationSpanish: ecuación | A mathematical sentence with an equals sign that shows two amounts are the same. | c = 24.95m means the total cost equals $24.95 times the number of months |
| variableSpanish: variable | A letter that represents a quantity that can change, or vary. | In c = 24.95m, the m can be 1, 2, or 12 — it varies. |
| rateSpanish: tasa | A fixed amount of one quantity for every one unit of the other quantity. | $24.95 for every 1 month — the amount attached to one unit. |
| representSpanish: representar | To show a relationship using a tool such as a table, a graph, or an equation. | graph → equation |
| define the variablesSpanish: definir las variables | To state exactly what quantity each letter in an equation stands for. | “Let m = months and c = total cost” — written before you solve. |
| ConstantSpanish: Constante | A number in an equation that never changes. | The 5 in y = 5x |
How it worksWorked examplewriting an equation from a situation
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A van rents for $16 an hour. Write an equation for the total cost, then find the cost of an 11-hour rental.
- Define the variables: h = hours rented, c = total cost in dollars.
- In words: the total cost equals the hourly rate times the number of hours.
- Write the rule with the constant rate in front: c = 16h.
- Substitute 11 for h: 16 × 11 → $176. The graph runs through (11, 176).
Answer: c = 16h, so an 11-hour rental costs $176.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A club charges $17 for each hoodie. Write an equation for the total cost, then find the cost of 20 hoodies.
- Define the variables: n = , t = .
- In words: the total cost equals times .
- Write the rule with the constant rate in front: t = n.
- Substitute 20 for n: × 20 → $ .
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I let stand for and stand for .
- In words, the total equals times .
- My equation is , so when x is , y is .
- This rule multiplies instead of adds because .
Word bank equationvariableconstant ratepermultiplyaddsubstituterepresentgraphpointtotaldefine
Watch outA common mistake
Writing the equation with addition — c = 24.95 + m — instead of multiplication. The fee is charged EVERY month, so the total is the rate times the number of months; always test the equation against a row of the table.
Lesson 9.3Equations from Situations
Apply Day · Version ASupported practice
Learning target I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.
-
1Complete each step, then write the final answer.
Scale the 1-unit column by the variable. A table shows 1 hour costs $5, 2 hours cost $10 and 3 hours cost $15. Let h = hours and c = total cost. Complete the equation: c = ___h.
Show your workHint How much does 1 hour cost? That number goes in the blank.
Final answer: -
2Complete each step, then write the final answer.
Use the same scale factor on both rows. Pens cost $2 each. Let p = pens and c = total cost. Write an equation. What do 8 pens cost?
Show your workHint Write c = 2p. Then put 8 in for p.
Final answer: -
3Complete each step, then write the final answer.
Scale the 1-unit column by the variable. A table shows 1 ticket costs $6, 2 tickets cost $12 and 4 tickets cost $24. Let t = tickets and c = total cost. Complete the equation: c = ___t.
Show your workHint How much does 1 ticket cost? That number goes in the blank.
Final answer:
Lesson 9.3Equations from Situations
Apply Day · Version BCore practice
Learning target I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.
-
1Circle the letter of the best answer. Show how you know.
Scaling multiplies; it does not add. A table shows 1 hour costs $6, 2 hours cost $12 and 3 hours cost $18. Leo writes c = 6 + h. Which equation is correct?
- Ac = 6h
- Bc = 6 + h
- Ch = 6c
Show your work -
2Complete each step, then write the final answer.
Go to 1 first, then scale up. A table shows 2 hours cost $34, 5 hours cost $85 and 7 hours cost $119. Let h = hours and c = total cost. Complete the equation: c = ___h.
Show your workFinal answer: -
3Complete each step, then write the final answer.
Scale the 1-unit column by the variable. A table shows 1 pound of apples costs $3, 2 pounds cost $6 and 3 pounds cost $9. Let p = pounds and c = total cost. Complete the equation: c = ___p.
Show your workFinal answer:
Lesson 9.3Equations from Situations
Apply Day · ChallengeExtension
Learning target I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.
-
1Circle the letter of the best answer. Show how you know.
Table A: when x = 1, 2, 3, y = 7, 14, 21. Table B: when x = 1, 2, 3, y = 7, 9, 11. Which equation matches Table B?
- Ay = 2x + 5
- By = 7x
- Cy = x + 6
- Dy = 9x
Show your work
-
2Circle the letter of the best answer. Show how you know.
A spin studio charges $7.50 for each class. Let n be the number of classes a member takes and let c be the total cost in dollars. Which equation represents the relationship?
- Ac = 7.5 + n
- Bn = 7.5c
- Cc = n ÷ 7.5
- Dc = 7.5n
Show your work -
3Complete each step, then write the final answer.
A skating rink charges $9 for 1 hour, $13 for 2 hours and $17 for 3 hours. Let h = hours and c = total cost. Complete the equation: c = 4h + ___.
Show your workFinal answer: