Graphing Proportional Relationships Indy Worksheet | PDF | Hot ... - Free Printable

Let's solve each problem step by step.

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Problem 1: Who eats more chips in 3 hours?

We are given:
- A graph showing Rebecca’s chip-eating rate.
- An equation for Leila: $ y = 15x $, where:
- $ x $ = number of hours
- $ y $ = number of chips eaten

We need to find out who eats more chips in 3 hours.

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#### Step 1: Find how many chips Rebecca eats in 3 hours

Look at the graph for Rebecca:

- The graph is a straight line passing through points like:
- (1, 12)
- (2, 24)
- (3, 36)
- (4, 48)
- (5, 60)

So, at $ x = 3 $ hours, $ y = 36 $ chips.

✔ Rebecca eats 36 chips in 3 hours.

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#### Step 2: Find how many chips Leila eats in 3 hours

Use the equation:
$ y = 15x $

Plug in $ x = 3 $:
$$
y = 15 \times 3 = 45
$$

✔ Leila eats 45 chips in 3 hours.

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#### Compare:
- Rebecca: 36 chips
- Leila: 45 chips

👉 Leila eats more chips in 3 hours.

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✔ Answer to Problem 1:

Leila eats more chips in 3 hours.

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Problem 2: Who uses sugar at a faster rate?

We are given:
- A graph for Erin, showing number of cups of tea vs. pounds of sugar used.
- An equation for Lucia: $ y = 10x $, where:
- $ x $ = pounds of sugar
- $ y $ = number of cups of tea

We want to know who uses sugar at a faster rate — that is, who makes more cups per pound of sugar.

This is a rate of cups per pound of sugar — so we compare the slope of each relationship.

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#### Step 1: Find Erin’s rate from the graph

From Erin’s graph:

Points on the line:
- (2, 6)
- (4, 12)
- (6, 18)
- (8, 24)
- (10, 30)

So, for every 2 pounds of sugar → 6 cups
→ Rate = $ \frac{6}{2} = 3 $ cups per pound

Or check another: $ \frac{12}{4} = 3 $, $ \frac{30}{10} = 3 $

✔ Erin’s rate = 3 cups per pound of sugar

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#### Step 2: Find Lucia’s rate from the equation

Given: $ y = 10x $

This means for every 1 pound of sugar ($ x = 1 $), she makes $ y = 10 $ cups.

So, Lucia’s rate = 10 cups per pound of sugar

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#### Compare rates:
- Erin: 3 cups per pound
- Lucia: 10 cups per pound

Since Lucia makes more cups per pound of sugar, she uses sugar at a faster rate (i.e., more efficiently or more intensely).

> Note: "Uses sugar at a faster rate" here means how many cups are made per unit of sugar — so higher value = faster rate of usage in terms of output per input.

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✔ Answer to Problem 2:

Lucia uses sugar at a faster rate.

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✔ Final Answers:

1. Leila eats more chips in 3 hours.
2. Lucia uses sugar at a faster rate.