Practice worksheet for calculating constant rate of change using tables and graphs.

Let's solve each problem step by step from the "Lesson 7 Skills Practice: Constant Rate of Change" worksheet.

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1. Find the constant rate of change for the table:

| Time Spent Mowing (h) | Money Earned ($) |
|------------------------|------------------|
| 1 | 10 |
| 3 | 30 |
| 5 | 50 |
| 7 | 70 |

Step:
Rate of change = $\frac{\text{Change in Money Earned}}{\text{Change in Time}}$

Use any two points, say (1, 10) and (3, 30):

$$
\frac{30 - 10}{3 - 1} = \frac{20}{2} = 10
$$

Check with another pair: (5, 50) and (7, 70):

$$
\frac{70 - 50}{7 - 5} = \frac{20}{2} = 10
$$

✔ Constant rate of change = $10 per hour

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2. Find the constant rate of change:

| Time (s) | Temperature (°F) |
|----------|------------------|
| 9:00 | 60 |
| 10:00 | 62 |
| 11:00 | 64 |
| 12:00 | 66 |

Time increases by 1 hour each time.

Temperature increases by 2°F per hour:

$$
\frac{62 - 60}{10:00 - 9:00} = \frac{2}{1} = 2
$$

Same for others: 64 - 62 = 2, 66 - 64 = 2

✔ Constant rate of change = 2°F per hour

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3. Find the constant rate of change:

| Number of Students | Number of Magazines Sold |
|--------------------|--------------------------|
| 10 | 150 |
| 20 | 300 |
| 25 | 375 |

Try between (10, 150) and (20, 300):

$$
\frac{300 - 150}{20 - 10} = \frac{150}{10} = 15
$$

Now check (20, 300) to (25, 375):

$$
\frac{375 - 300}{25 - 20} = \frac{75}{5} = 15
$$

✔ Constant rate of change = 15 magazines per student

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4. Find the constant rate of change:

| Number of Trees | Number of Apples |
|-----------------|------------------|
| 5 | 100 |
| 10 | 200 |
| 15 | 300 |
| 20 | 400 |

From (5, 100) to (10, 200):

$$
\frac{200 - 100}{10 - 5} = \frac{100}{5} = 20
$$

(10, 200) to (15, 300): $\frac{100}{5} = 20$

(15, 300) to (20, 400): $\frac{100}{5} = 20$

✔ Constant rate of change = 20 apples per tree

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5. Find the constant rate of change for the graph (Temperature vs. Hours)

The graph shows temperature decreasing over time.

We can pick two points on the line.

Assume the graph goes from:
- At 0 hours: 80°F
- At 4 hours: 40°F

So, change in temp = $40 - 80 = -40$°F
Change in time = $4 - 0 = 4$ hours

$$
\text{Rate} = \frac{-40}{4} = -10
$$

✔ Constant rate of change = -10°F per hour

*(Note: Negative because temperature is decreasing)*

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6. Find the constant rate of change for the graph (Heat Consumption vs. Number of People)

Graph shows a straight line from:
- 0 people → 0 units of heat
- 4 people → 120 units of heat

So:
$$
\text{Rate} = \frac{120 - 0}{4 - 0} = \frac{120}{4} = 30
$$

✔ Constant rate of change = 30 units of heat per person

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✔ Final Answers:

1. $10 per hour
2. 2°F per hour
3. 15 magazines per student
4. 20 apples per tree
5. -10°F per hour
6. 30 units of heat per person

These represent constant rates of change, meaning the relationship is linear and the ratio between changes is consistent.

Let me know if you'd like these explained visually or with graphs!