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Grade 8 · lesson 1 of 4

Connect a rule, table and rate

Interpret the fixed part and changing part of a linear function.

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Supplied materials

  • Fictional printing booth: one order costs a $3 setup fee plus $2 for each poster.
  • Let x be the number of posters, a nonnegative whole number, and y be the total cost in dollars.

Learn the idea

A linear cost rule here is y = 2x + 3. The coefficient 2 is the increase for each extra poster; the constant 3 is the fee that does not depend on poster count.

Check the rule with a table. The change in y for one additional poster is constant, but the ratio y/x is not constant because the setup fee remains. The real input domain is whole poster counts, not negative or fractional posters.

  1. Use the rule to make a table for x = 1, 2 and 3.
  2. Check that each extra poster adds $2.
  3. Calculate the cost for 4 posters.
  4. Use the changed rule in the question and compare its fixed fee.
Worked example

See the method in action

For x = 1, 2, 3, the totals are $5, $7, $9. For 4 posters, y = 2 × 4 + 3 = $11. A zero-poster input gives $3 in the mathematical rule; whether a real booth accepts such an order is a separate policy.

Your turn

Check your reasoning

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A second booth uses y = 3x + 1. How much does an order of 4 posters cost there?

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See the answer and explanation

$13

Substitute x = 4 into the second rule: 3 × 4 + 1 = $13. The coefficient is a per-poster rate, and the 1 is added once.

Take it further

Compare the booths at 2 and 5 posters. Check: both cost $7 at two; the first costs $13 and the second $16 at five.

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Longer courses for learners ages 14+

These related courses have their own preparation and projects. They are not early-grade assignments.

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