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The table shows Elena's profit based on the number of cookies sold, and the task is likely to involve identifying a pattern or relationship between the number of cookies sold and the profit.

Let's analyze the dataThe table shows Elena's profit based on the number of cookies sold, and the task is likely to involve identifying a pattern or relationship between the number of cookies sold and the profit.

Let's analyze the 

| Number of Cookies Sold | Profit (dollars) |
|------------------------|------------------|
| 4                      | -1.50            |
| 5                      | 1.25             |
| 6                      | 4.00             |
| 7                      | 6.75             |

### Step 1: Find the rate of change (slope)
To determine how much Elena's profit increases for each additional cookie sold, we can calculate the difference between consecutive profits:

- From 4 to 5 cookies: $1.25 - (-1.50) = 2.75$
- From 5 to 6 cookies: $4.00 - 1.25 = 2.75$
- From 6 to 7 cookies: $6.75 - 4.00 = 2.75$

The profit increases by $2.75 for every additional cookie sold, suggesting a linear relationship between the number of cookies sold and the profit.

### Step 2: Equation of the line
The profit $ P $ depends on the number of cookies sold $ x $. The slope (rate of change) is $2.75 per cookie. To find the equation, we can use the point-slope form of a linear equation:

\[
P = mx + b
\]

Where:
- $ m $ is the slope, $ m = 2.75 $
- $ b $ is the y-intercept (the profit when no cookies are sold).

Using the point $ (4, -1.50) $, substitute into the equation:

\[
-1.50 = 2.75(4) + b
\]
\[
-1.50 = 11 + b
\]
\[
b = -1.50 - 11 = -12.50
\]

Thus, the equation is:

\[
P = 2.75x - 12.50
\]

This equation represents Elena's profit as a function of the number of cookies sold.

Would you like further explanation or have any other questions?

Here are five related questions for practice:
1. How much profit will Elena make if she sells 10 cookies?
2. If Elena needs to make a $0 profit, how many cookies should she sell?
3. What does the y-intercept represent in this context?
4. How would the profit change if the slope were $3.00 instead of $2.75?
5. How many cookies would Elena need to sell to make a profit of $20?

**Tip:** The slope in a linear equation tells you how much the dependent variable (profit, in this case) changes with each unit increase in the independent variable (number of cookies sold).

Elena is selling cookies at a constant price to raise money for charity. The table shows her profit based on the number of cookies sold: 4 cookies = -1.50 dollars, 5 cookies = 1.25 dollars, 6 cookies = 4.00 dollars, 7 cookies = 6.75 dollars.

Learn how to determine the relationship between the number of cookies sold and the profit Elena makes. This problem covers algebraic concepts such as linear relationships and the slope-intercept form, with a step-by-step solution to find the equation P = 2.75x - 12.50. Suitable for Grades 7-9.

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