Testinar Grade 7 math

Graphing Proportional Relationships

Students will build Grade 7 mastery of graphing proportional relationships using models, equations, and test-style reasoning.

CH01-05 Ratios and Proportional Relationships
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. The graph shows a proportional relationship between hours worked and dollars earned. It passes through the origin and the point \((2,30)\). What is the unit rate (dollars per hour)?

    1. \($2\) per hour
    2. \($60\) per hour
    3. \($28\) per hour
    4. \($15\) per hour

  2. The graph shows a proportional relationship. What is the unit rate (the value of \(y\) at \(x=1\))?

    Graphing Proportional Relationships visual for G7-C01-T05-Q002
    1. \(5\)
    2. \(1\)
    3. \(2\)
    4. \(0.5\)

  3. Maya runs at a constant speed. The relationship between distance (miles) and time (hours) is proportional and passes through \((3, 18)\). How far does she run per hour?

    1. \(3\) miles per hour
    2. \(54\) miles per hour
    3. \(15\) miles per hour
    4. \(6\) miles per hour

  4. A car drives at a constant speed shown by this graph with unit-rate point \((1, 0.8)\). Which equation represents this relationship?

    Graphing Proportional Relationships visual for G7-C01-T05-Q004
    1. \(y = 8x\)
    2. \(y = 1.25x\)
    3. \(y = 5x\)
    4. \(y = 0.8x\)

  5. A recipe for lemonade uses a constant ratio of sugar to water. The graph shows a proportional relationship that passes through the point \((4,6)\), where \(x\) = cups of sugar and \(y\) = cups of water. How many cups of water are needed for 8 cups of sugar?

    1. \(6\) cups
    2. \(8\) cups
    3. \(10\) cups
    4. \(12\) cups

  6. Which equation represents this proportional relationship?

    Graphing Proportional Relationships visual for G7-C01-T05-Q006
    1. \(y = 10x\)
    2. \(y = 1.4x\)
    3. \(y = 7x\)
    4. \(y = 0.7x\)

  7. A book club orders books in bulk at a constant price per book. If 10 books cost \($120\), how much do 15 books cost?

    1. \($80\)
    2. \($120\)
    3. \($180\)
    4. \($1200\)

  8. A store sells apples at a constant unit price. A customer buys 6 apples for \($4.50\). How much does one apple cost?

    1. \($0.50\)
    2. \($2.25\)
    3. \($1.50\)
    4. \($0.75\)
Teacher and parent reference

Answer key and explanations

  1. D. \($15\) per hour

    The unit rate is the \(y\)-value when \(x=1\). Because \((2,30)\) is on the line through the origin, \(k=30/2=15\), so earning rate is \($15\) per hour.

  2. D. \(0.5\)

    A proportional relationship passes through the origin. The marked point is \((2,1)\), so the unit rate \(k = 1/2 = 0.5\). The line equation is \(y = 0.5x\).

  3. D. \(6\) miles per hour

    From the point \((3,18)\), the unit rate is \(18 \div 3 = 6\) miles per hour.

  4. D. \(y = 0.8x\)

    The unit-rate point \((1, 0.8)\) shows \(k = 0.8\), so the equation is \(y = 0.8x\).

  5. D. \(12\) cups

    The unit rate is \(6 \div 4 = 1.5\). So \(y = 1.5x\). At \(x = 8\), \(y = 1.5 \times 8 = 12\) cups.

  6. D. \(y = 0.7x\)

    The unit-rate marker at \((1, 0.7)\) shows \(k = 0.7\). So the equation is \(y = 0.7x\).

  7. C. \($180\)

    Unit rate is \($120 \div 10 = $12\) per book. For 15 books: \(15 \times $12 = $180\).

  8. D. \($0.75\)

    Unit price = \($4.50 \div 6 = $0.75\) per apple.

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