Type the correct answer in each box. If necessary, use / for the fraction bar(s).
Emily works at a perfumery. She extracts 3 liters of essential oil for perfumes in 2 days.
 Assuming Emily extracts essential oil at a constant rate, we can graph this relationship with time in days along the x-axis and quantity of oil in liters along the y-axis. The slope of the line representing this relationship is  ?
.
A point on this line that corresponds to the amount of oil Emily extracts after 5 days is (5, 
?).

To find the slope of the line representing the relationship between time and the amount of essential oil Emily extracts, we use the fact that she extracts 3 liters in 2 days. The slope \( m \) is the rate of extraction in liters per day.

\[ m = \frac{\text{change in quantity}}{\text{change in time}} = \frac{3 \text{ liters}}{2 \text{ days}} = \frac{3}{2} \text{ liters per day} \]

So, the slope \( m \) is \( \frac{3}{2} \).

Next, we need to find the amount of oil extracted after 5 days. Using the slope, we can calculate this as follows:

\[ \text{Quantity of oil after 5 days} = 5 \times \frac{3}{2} = \frac{15}{2} = 7.5 \text{ liters} \]

So, the point on the line after 5 days is \( (5, 7.5) \).

- The slope of the line is \( \frac{3}{2} \).
- A point on this line after 5 days is \( (5, 7.5) \).

Would you like more details or have any questions?

Here are some questions you might find interesting:
1. How do you determine the slope of a line from two points?
2. What is the formula for the slope-intercept form of a line?
3. How do you convert a rate into a unit rate?
4. What other information can you derive from the slope of a line?
5. How can you graphically interpret the y-intercept of a line?

**Tip:** When working with slopes and rates, always make sure your units are consistent to avoid errors in your calculations.

Learn how to calculate the rate of change and graph linear equations with a step-by-step explanation. This problem involves understanding the rate of extraction, graphing the relationship between time and quantity of oil, and calculating the slope of the line. Suitable for students in Grades 7-9.

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