Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.3Equations from Situations

Apply Day · Set BSecond form · new problems, same idea

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

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

Remember9.3 · Part II

Writing Two-Variable Equations

  1. Identify the independent variable (x) and dependent variable (y)
  2. Find the constant unit rate (k = y ÷ x)
  3. Write the equation relating the two variables: y = kx (or y = x + c)

Words: equation (ecuación)variable (variable)rate (tasa)represent (representar)define the variables (definir las variables)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    In the equation c = 24.95m for the gym membership, what does m represent?

    1. AThe number of months of membership
    2. BThe total cost in dollars
    3. CThe monthly fee of $24.95
    4. DThe name of the gym
    Show your work
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    Books1bTotal cost ($)4?× b× b
    Scale the 1-unit column by the variable.

    A table shows 1 book costs $4, 2 books cost $8 and 3 books cost $12. Let b = books and c = total cost. Complete the equation: c = ___b.

    Show your work
    Final answer:
  2. 3Complete each step, then write the final answer.
    Time (months)1mTotal cost ($)12.99?× m× m
    Scale the 1-unit column by the variable.

    A music plan costs $12.99 for 1 month, $25.98 for 2 months and $38.97 for 3 months. Let m = months and c = total cost. Complete the equation: c = ___m.

    Show your work
    Final answer:
  3. 4Complete each step, then write the final answer.

    A gym charges $35 for 1 month, $55 for 2 months and $75 for 3 months. Let m = months and c = total cost. Complete the equation: c = 20m + ___.

    Show your work
    Final answer:
  4. 5Complete each step, then write the final answer.
    0123456071421283542Days (x)Cups of food (y)(0, 0)(2, 14)(3, 21)(5, 35)

    A graph shows cups of dog food. It goes through (2, 14), (3, 21) and (5, 35). Let x = days and y = cups. Complete the equation: y = ___x.

    Show your work
    Final answer:
  5. 6Complete each step, then write the final answer.

    A plant is 4 cm tall when it is planted. It grows 3 cm each week. Let w = weeks and p = height in cm. Write an equation. How tall is the plant after 6 weeks?

    Show your work
    Final answer:
  6. 7Complete each step, then write the final answer.

    A boat rental has a fixed fee plus a cost per hour. 2 hours cost $31 and 5 hours cost $61. Let h = hours and c = total cost. Write the equation. What is the fixed fee?

    Show your work
    Final answer:
  7. 8Circle the letter of the best answer. Show how you know.

    Recreation World charges $24.95 per month. What is the total cost of 2 months of membership?

    1. A$24.95
    2. B$26.95
    3. C$49.90
    4. D$74.85
    per 1
  8. 9Circle the letter of the best answer. Show how you know.

    A canoe rents for $15 per hour. Let h = hours and c = total cost. Which equation represents the relationship?

    1. Ac = 15h
    2. Bc = 15 + h
    3. Ch = 15c
    4. Dc = h − 15
    Show your work
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help