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Cogito

Integrated Math 1 · Chapter 2 · Lesson 1

Practice Worksheet

Slope and Rate of Change

How fast one thing changes with another.

12 problems · about 21 minutes · F-IF.B.6, S-ID.C.7

NameDate

Figure — use these to answer the problems

Change the slope and watch the two triangles. Both give the same ratio, which is why slope is one number.
-10-10-5-55510101236
y = 2x + 1
Slope2
y-intercept1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Through (2, 4) and (6, 16). What is the slope?

    Answer

  2. What makes a relationship linear?

    • The rate of change never varies.
    • The values always increase.

  3. Through (0, 0) and (2, 6). Slope?

    Answer

  4. Through (1, 5) and (3, 5). Slope?

    Answer

  5. Through (2, 8) and (5, 2). Slope?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Through (−1, 2) and (3, 10). Slope?

    Answer

  2. A horizontal line. What is its slope?

    Answer

  3. Through (4, 1) and (4, 9). Is the slope defined? 1 yes, 0 no.

    Answer

Stretch Yourself

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

4 problems

  1. Sort each slope by the direction of the line.

    Write each item under the heading it belongs to: Slope 4 · Slope 0.5 · Slope −3 · Slope −0.2

    Rises left to right

    Falls left to right

  2. Through (0, 7) and (4, 3). Slope?

    Answer

  3. The Two Points

    Through (1, 3) and (4, 12). What is the slope?

    Answer

  4. The Taxi

    $8 for 2 miles and $20 for 8 miles. Cost per mile, in dollars?

    Answerdollars