Worksheet for identifying independent and dependent variables in linear relationships.

It looks like you've uploaded an image of a worksheet titled "Getting Started with Linear Relations", which asks students to determine whether each given pair of variables is independent or dependent. The task is to identify, for each scenario, which variable is independent (the one that is controlled or changed) and which is dependent (the one that changes in response).

Let’s go through each pair and explain the reasoning.

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1. Cell Phone Bill

- Independent: How much you talk/texting on your phone
- Dependent: How much you make

✘ This pair is incorrectly matched. Let's fix it.

Actually:
- Independent: How much you talk/texting on your phone
- Dependent: How much you pay (the bill)

✔ Corrected:
- Independent: How much you talk/texting on your phone
- Dependent: Cell Phone Bill (amount you pay)

> 💡 *Reason*: Your usage affects the cost of the bill.

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2. The amount of gas you have

- Independent: The amount of gas you have
- Dependent: Minutes used

✘ This doesn't make logical sense. "Minutes used" isn't directly dependent on gas amount unless we're talking about time spent driving.

But if we interpret this as:
- Independent: The amount of gas you have
- Dependent: How far you can drive (or how long you can drive)

Then it makes sense.

But here, the dependent variable listed is "Minutes Used", which is ambiguous.

Let’s assume it's referring to time you can drive.

So:
- Independent: The amount of gas you have
- Dependent: Time it takes to drive somewhere

✔ That could work — more gas → longer drive time.

> 💡 *Reason*: The amount of gas determines how long you can drive.

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3. Who scores more points

- Independent: Who scores more points
- Dependent: Time it takes to drive somewhere

✘ This is unrelated.

This seems mismatched. "Who scores more points" is likely a result of a game, not related to driving time.

Let’s look at the correct pairing:

Perhaps the intended pair is:
- Independent: Time it takes to drive somewhere
- Dependent: How fast you drive?

But that's backwards.

Wait — let’s re-express the list properly.

Looking at the table:

| Independent | Dependent |
|-------------|-----------|
| Cell Phone Bill | How much you make |
| How much you talk/texting on your phone | The amount of assignment you turned in |
| The amount of gas you have | Minutes Used |
| Who scores more points | Time it takes to drive somewhere |
| Your Grade | Cost of a speeding ticket |
| Winner of a football game | How far you can drive |
| Temperature | HOW MANY PAY YOU WONT OVER $500/3 LIMIT |
| The hours you work | How fast you drive |

This table has several mismatches and typos.

Let’s go through each row correctly.

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Correct Analysis:

#### 1. Cell Phone Bill vs. How much you make
- ✘ Not related.
- But if the independent is how much you talk/text, then cell phone bill is dependent.

✔ So:
- Independent: How much you talk/texting on your phone
- Dependent: Cell Phone Bill

> ✔ This is a valid pair.

#### 2. How much you talk/texting on your phone vs. The amount of assignment you turned in
- ✘ No logical connection.
- These are unrelated variables.

🚫 Invalid pair.

#### 3. The amount of gas you have vs. Minutes Used
- Possibly: Amount of gas → how long you can drive (minutes)
- So:
- Independent: The amount of gas you have
- Dependent: Minutes used (driving time)

✔ Makes sense.

#### 4. Who scores more points vs. Time it takes to drive somewhere
- ✘ Completely unrelated.

🚫 Invalid.

#### 5. Your Grade vs. Cost of a speeding ticket
- ✘ No connection.

🚫 Invalid.

#### 6. Winner of a football game vs. How far you can drive
- ✘ Unrelated.

🚫 Invalid.

#### 7. Temperature vs. HOW MANY PAY YOU WONT OVER $500/3 LIMIT
- This sentence is garbled. Likely meant to be:
- "How many people will pay you won’t exceed $500 over 3 months?"
- Or possibly: “How many paychecks will you get over $500?”

But still, temperature doesn’t affect paycheck amounts.

🚫 Invalid.

#### 8. The hours you work vs. How fast you drive
- ✘ No direct relationship.

🚫 Invalid.

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Conclusion: Many of these pairs are incorrectly matched.

But based on logic, here are the correct independent-dependent pairs from the list:

| Independent Variable | Dependent Variable | Reason |
|----------------------|--------------------|--------|
| How much you talk/text on your phone | Cell Phone Bill | Usage affects cost |
| The amount of gas you have | Minutes used (driving time) | More gas = longer driving time |
| The hours you work | How much you make | Hours worked determine income |
| How fast you drive | Time it takes to drive somewhere | Speed affects travel time |
| How far you can drive | Amount of gas you have | Gas limits distance |
| Your grade | The amount of assignment you turned in? | Actually, assignments affect grades, so reverse: assignments → grade |

Wait — let’s fix this.

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Correct Pairings (Based on Logic):

Let’s reorganize the correct relationships:

1. Independent: How much you talk/text
Dependent: Cell Phone Bill
→ Usage affects cost.

2. Independent: The amount of gas you have
Dependent: How far you can drive / Minutes used
→ More gas → longer drive.

3. Independent: The hours you work
Dependent: How much you make
→ Work hours determine income.

4. Independent: How fast you drive
Dependent: Time it takes to drive somewhere
→ Higher speed = less time.

5. Independent: The amount of assignment you turned in
Dependent: Your Grade
→ Assignments affect your grade.

6. Independent: Winner of a football game
Dependent: Who scores more points
→ Winner is determined by who scored more.

7. Independent: Temperature
Dependent: ? (Not clear) — perhaps how many people wear jackets?

But none of the given options make sense.

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Final Answer: Based on the worksheet, the most logical correct pairs are:

| Independent | Dependent |
|-------------|----------|
| How much you talk/texting on your phone | Cell Phone Bill |
| The amount of gas you have | Minutes used (driving time) |
| The hours you work | How much you make |
| How fast you drive | Time it takes to drive somewhere |
| The amount of assignment you turned in | Your Grade |
| Who scores more points | Winner of a football game |

But the original table has many errors.

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Summary:

✔ Corrected Table:

| Independent | Dependent |
|------------|----------|
| How much you talk/texting on your phone | Cell Phone Bill |
| The amount of gas you have | Minutes used |
| The hours you work | How much you make |
| How fast you drive | Time it takes to drive somewhere |
| The amount of assignment you turned in | Your Grade |
| Who scores more points | Winner of a football game |

✘ Incorrect pairs:
- "Cell Phone Bill" as independent → no, it's dependent.
- "Who scores more points" → "Time to drive" → unrelated.
- "Your Grade" → "Cost of speeding ticket" → unrelated.

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Final Advice:

The worksheet contains several incorrect pairings. To solve it correctly, match variables where one causes or influences the other.

Key Rule:
- Independent variable: what you control or change.
- Dependent variable: what changes as a result.

For example:
- You choose how many hours to work → how much you make depends on that.

Let me know if you'd like a corrected version of the worksheet!