https://file.aiquickdraw.com/mathbot/file/1726268298618wsch9723.jpg

We need to calculate how much more Sofia earns per hour compared to Elizabeth by determining their hourly rates.

### Step 1: Calculate Sofia's hourly rate

From the graph, we see two points that describe Sofia's earnings:

- (10, 218): Sofia earned $218 after 10 hours.
- (20, 436): Sofia earned $436 after 20 hours.

The slope of this line represents Sofia's hourly rate. The slope formula is:
\[
\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}
\]
Using the points (10, 218) and (20, 436):
\[
\text{slope} = \frac{{436 - 218}}{{20 - 10}} = \frac{{218}}{{10}} = 21.8
\]
So, Sofia earns **$21.80 per hour**.

### Step 2: Calculate Elizabeth's hourly rate

We are given that Elizabeth earned $492.80 in 28 hours. Her hourly rate is:
\[
\text{Hourly rate} = \frac{{492.80}}{{28}} = 17.60
\]
So, Elizabeth earns **$17.60 per hour**.

### Step 3: Compare Sofia's and Elizabeth's hourly rates

To find how much more Sofia earns per hour than Elizabeth:
\[
\text{Difference} = 21.80 - 17.60 = 4.20
\]
So, **Sofia earns $4.20 more per hour than Elizabeth**.

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Would you like more details or further clarification? 

Here are five related questions to expand on this problem:
1. How many total hours would Sofia need to work to earn $1,000?
2. If Elizabeth worked 35 hours, how much would she earn?
3. What is the equation of the line representing Sofia's earnings?
4. How long would it take for both friends to earn the same amount if Sofia works fewer hours than Elizabeth?
5. How much would Elizabeth earn if she worked the same number of hours as Sofia in the graph (20 hours)?

**Tip:** When comparing rates or slopes from a graph, always look for clear points and apply the slope formula to calculate the rate of change accurately.

How much more does Sofia earn per hour than Elizabeth?

Learn how to calculate and compare hourly earnings using slope and linear equations. In this problem, Sofia earns $21.80 per hour, while Elizabeth earns $17.60 per hour. Find out how much more Sofia earns per hour and apply linear functions to real-world scenarios. Suitable for Grades 7-9.

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