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Linear Equations Introduction

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Linear Equations Introduction

A community fair is setting up a game booth. Use linear equations to model costs, find unknown values, and check whether a plan works. Show your thinking for written answers.

Read the rule

The booth charges $4 to play, plus $3 for each round. Let x be the number of rounds and y be the total cost in dollars. The rule is y = 3x + 4.

1.In y = 3x + 4, which number is the coefficient of x?

2.In this rule, what does the constant 4 represent?

3.How much does it cost to play 5 rounds? Substitute x = 5 into y = 3x + 4 and show the calculation.

Build and compare equations

The booth is adding a prize wheel. Keep track of the rate per round and any starting amount.

4.A second game charges $2 per round and has no starting fee. Write an equation for total cost y after x rounds.

5.Match each equation part in y = 6x + 9 with its description.

Cost added for each round
Total cost
Number of rounds
Starting amount

6.Two plans are available: Plan A costs y = 3x + 4 dollars, and Plan B costs y = 5x. For x = 3 rounds, which plan costs less, and by how much?

Solve the mystery cost

Use inverse operations to find the missing number of rounds. Check each answer in the original equation.

7.For the rule y = 3x + 4, the total is $25. Find x, the number of rounds. Write an equation and solve it.

8.Solve 4x + 6 = 30. Show the step that removes 6, then the step that removes the factor of 4.

9.A helper says the solution to 2x + 7 = 19 is x = 5. Is the claim correct? Substitute 5 into the left side and explain.

10.Invent a fair-booth situation with a starting fee and a cost per round. Write a linear equation, state what x and y represent, then find y when x = 4.