Algebra worksheet focusing on rate of change and slope with tables, graphs, and equations.

Let’s solve the problem step by step.

There are two main parts:
Problem 1 (renting a movie) and Problem 2 (amusement park admission), each with two subparts:
a. Find the rate of change (slope)
b. Interpret the meaning of that rate

We’ll handle them one at a time.

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Problem 1: Movie Rental

Table:

| Time (hours) | Rent Cost (dollars) |
|--------------|---------------------|
| 1 | 3.00 |
| 2 | 5.00 |
| 3 | 7.00 |
| 4 | 9.00 |

This is linear — cost increases by $2 for each extra hour.

#### a. Rate of change = (change in cost) / (change in time)

Pick any two points — say (1, 3) and (4, 9):

Change in cost = 9 − 3 = 6
Change in time = 4 − 1 = 3
Rate = 6 / 3 = $2 per hour

Check with another pair: (2, 5) and (3, 7):
7 − 5 = 2, 3 − 2 = 1 → 2/1 = $2/hour ✔

So rate of change = $2 per hour

#### b. Interpretation:
The cost to rent a movie increases by $2 for every additional hour you keep it.

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Problem 2: Amusement Park Admission

Table:

| Time (hours) | Admission Fee ($) |
|--------------|-------------------|
| 2 | 20.00 |
| 4 | 30.00 |
| 6 | 40.00 |

Again, looks linear.

#### a. Rate of change:

Use points (2, 20) and (6, 40):

Change in fee = 40 − 20 = 20
Change in time = 6 − 2 = 4
Rate = 20 / 4 = $5 per hour

Check with (2,20) and (4,30):
30 − 20 = 10, 4 − 2 = 2 → 10/2 = $5/hour ✔

So rate of change = $5 per hour

#### b. Interpretation:
The admission fee increases by $5 for every additional hour spent at the park.

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Now, the last part says:

> Calculate the slope of each line. Write your answer in simplest form.

We already did that:
- Movie rental: slope = 2
- Amusement park: slope = 5

(These are just the rates of change we found.)

Also, there are four graphs labeled 1–4 at the bottom. Since no specific question is asked about them (e.g., “match each graph to a situation”), and the instruction only says “Calculate the slope of each line”, but no lines are labeled with coordinates — and the tables above correspond to two situations — likely the expectation is just to give the two slopes.

But looking again: the worksheet has four graphs (1 to 4), and possibly expects matching or slope calculation from graphs. However, since the user didn’t provide coordinate values for the graphs (and we can’t see them), and the only data given are the two tables, the only computable slopes are from those tables.

Given standard curriculum design, the four graphs likely represent different slopes (e.g., positive, negative, zero, undefined), but without visual data, we cannot compute slopes from graphs here.

Since the only explicit instructions with numbers are Problems 1 and 2, and the final line says “Calculate the slope of each line” — and there are two lines (one per situation), the answer should be:

- Slope for movie rental: 2
- Slope for amusement park: 5

Let me double-check units and arithmetic once more:

Movie:
- From 1h → 2h: $5 − $3 = $2 increase → $2/h
- 2h → 3h: $7 − $5 = $2 → same
✔ Consistent

Amusement park:
- 2h → 4h: $30 − $20 = $10 over 2h → $5/h
- 4h → 6h: $40 − $30 = $10 over 2h → $5/h
✔ Consistent

All correct.

Final Answer:
2 and 5