Linear Relationships Project worksheet on calculating fair expenses with equations, tables, and graphs.

Let's solve this step-by-step based on the information provided in the image.

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Problem Summary:

Joel is going to the State Fair of Texas.
- Admission cost: $28.50
- Each additional ride or food ticket costs: $3.50

We are to:
1. Write an equation for total cost.
2. Define what x and y represent.
3. Complete a table.
4. Graph the situation.
5. Determine if the relationship is proportional or non-proportional.
6. Calculate total cost for 25 tickets.

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Step 1: Write an Equation

Let:
- $ x $ = number of additional ride/food tickets Joel buys
- $ y $ = total amount of money Joel spends

The total cost includes:
- A fixed admission fee: $28.50
- Plus $3.50 per ticket: $3.50 × x

So, the equation is:

$$
y = 3.50x + 28.50
$$

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Step 2: Define Variables

- The x variable represents: The number of additional ride or food tickets Joel purchases.
- The y variable represents: The total amount of money Joel spends at the fair.

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Step 3: Complete the Table

Use the equation $ y = 3.50x + 28.50 $

| x (tickets) | y (total cost) |
|-------------|----------------|
| 0 | $3.50(0) + 28.50 = 28.50$ |
| 2 | $3.50(2) + 28.50 = 7.00 + 28.50 = 35.50$ |
| 6 | $3.50(6) + 28.50 = 21.00 + 28.50 = 49.50$ |
| 10 | $3.50(10) + 28.50 = 35.00 + 28.50 = 63.50$ |
| 14 | $3.50(14) + 28.50 = 49.00 + 28.50 = 77.50$ |

Completed Table:

| x | y |
|---|--------|
| 0 | 28.50 |
| 2 | 35.50 |
| 6 | 49.50 |
| 10| 63.50 |
| 14| 77.50 |

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Step 4: Graph the Situation

Plot the points from the table on a coordinate plane:
- Points: (0, 28.50), (2, 35.50), (6, 49.50), (10, 63.50), (14, 77.50)

Draw a straight line through these points. This is a linear graph with:
- Y-intercept at (0, 28.50)
- Slope of 3.50 (rise over run)

> Since you can't draw here, just describe it: Start at (0, 28.50), then go up 3.5 units for every 1 unit right.

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Step 5: Is the Relationship Proportional or Non-Proportional? Why?

- Non-proportional

Why?
A proportional relationship must pass through the origin (0,0). But here, when $ x = 0 $, $ y = 28.50 $, not 0. That means there's a fixed cost (admission) even if no tickets are bought.

So, because of the fixed admission fee, the relationship is non-proportional.

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Step 6: If Joel wanted to purchase 25 food/ride tickets, how much would he spend?

Use the equation:
$$
y = 3.50x + 28.50
$$
Plug in $ x = 25 $:

$$
y = 3.50(25) + 28.50 = 87.50 + 28.50 = 116.00
$$

✔ Answer: Joel would spend $116.00 in total.

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✔ Final Answers:

- Equation: $ y = 3.50x + 28.50 $
- x represents: Number of additional ride/food tickets
- y represents: Total money spent
- Table completed as shown above
- Graph: Linear line starting at (0, 28.50), slope = 3.50
- Proportional? No — because it does not pass through the origin (has a y-intercept ≠ 0)
- Total for 25 tickets: $116.00

Let me know if you'd like a visual graph description or help turning this into a printable worksheet!