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Cogito

Integrated Math 1 · Chapter 2 · Lesson 3

Practice Worksheet

Modelling with Linear Functions

Turning a situation into an equation.

12 problems · about 21 minutes · F-LE.A.1, F-LE.B.5

NameDate

Figure — use these to answer the problems

Set the intercept to a fixed fee and the slope to a per-unit charge. The line is the whole cost model.
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y = 3x + 2
Rate per unit3
Fixed fee2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. $40 fee plus $6 an hour. Cost for 5 hours, in dollars?

    Answer

  2. In a cost model, what does the y-intercept represent?

    • The fixed amount charged before any units are used.
    • The charge per unit.

  3. C = 5x + 12. What is the fixed amount?

    Answer

  4. C = 5x + 12. What is the rate per unit?

    Answer

  5. C = 5x + 12 at x = 8. What is C?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. $25 joining fee plus $10 a month. Cost after 4 months, in dollars?

    Answer

  2. A tank holds 100 L and drains 4 L a minute. Litres after 10 minutes?

    Answer

  3. For a model counting tickets sold, is x = 2.5 in the domain? 1 yes, 0 no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the modelling steps in order.

    Write 1 to 4 in the boxes to put these in order.

    • Identify the fixed starting amount.
    • Identify the rate per unit.
    • Write the equation combining both.
    • State which input values make sense.

  2. C = 2x + 40 at x = 15. What is C?

    Answer

  3. The Plan

    C = 0.10m + 20. What is the cost for 300 minutes, in dollars?

    Answerdollars

  4. The Fee

    A gym charges $30 to join plus $15 a month. Cost after 6 months, in dollars?

    Answerdollars