Linear Equations Relationship Real World Project - Write/Graph/Solve/Table - Free Printable

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:
- X-axis: Number of tickets (x)
- Y-axis: Total cost (y)

Points to plot:
- (0, 28.50)
- (2, 35.50)
- (6, 49.50)
- (10, 63.50)
- (14, 77.50)

Draw a straight line through these points. It will be a linear graph with a y-intercept at (0, 28.50) and a slope of 3.50.

> Note: Since this is a text-based response, I can't draw the graph here, but you would plot the points and connect them with a straight line.

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

A proportional relationship has:
- A constant ratio between y and x
- Passes through the origin (0,0)

But here:
- When $ x = 0 $, $ y = 28.50 $ → Does NOT pass through the origin
- There’s a fixed cost (admission), so even with 0 tickets, Joel still pays $28.50

✔ Therefore, this is a non-proportional linear relationship.

Answer:
Non-proportional, because there is a fixed admission fee ($28.50) that does not depend on the number of tickets. The graph does not go through the origin.

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Step 6: How much would Joel spend for 25 tickets?

Use the equation:

$$
y = 3.50x + 28.50
$$

Plug in $ x = 25 $:

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

✔ Total cost: $116.00

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✔ Final Answers:

#### Equation:
$$
y = 3.50x + 28.50
$$

#### Variable Definitions:
- $ x $: Number of additional ride/food tickets
- $ y $: Total money spent at the fair

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

#### Graph:
- Plot the points above and draw a straight line starting at (0, 28.50) with a slope of 3.50.

#### Proportional or Not?
- Non-proportional — because it does not pass through the origin due to the fixed admission fee.

#### Cost for 25 Tickets:
- $116.00

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Let me know if you'd like a visual version of the graph or help formatting this into a printable answer sheet!