Question

money earned vs. bookmarks sold
ellen makes and sells bookmarks. she graphs the number of bookmarks sold compared to the total money earned. what is the rate of change for the function graphed to the left?

• \\(\frac{2}{5}\\)
• \\(\frac{5}{4}\\)
• \\(\frac{5}{3}\\)
• \\(\frac{5}{2}\\)

Explanation:

🆕 New Concept Discovered: Rate of Change
How fast one quantity changes compared to another.

Step 1: Identify coordinates from the graph

We can choose any two points plotted on the line to find the rate of change:

• Point 1: \( (x_1, y_1) = (4, 0) \)
• Point 2: \( (x_2, y_2) = (8, 10) \)

Step 2: Apply the rate of change formula

The rate of change (or slope) measures how much the vertical value (\(y\), money earned) changes for every unit increase in the horizontal value (\(x\), bookmarks sold):

$$ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} $$

Substitute the coordinates into the formula:

$$ \text{Rate of Change} = \frac{10 - 0}{8 - 4} $$

$$ \text{Rate of Change} = \frac{10}{4} $$

Step 3: Simplify the fraction

Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is \(2\):

$$ \frac{10 \div 2}{4 \div 2} = \frac{5}{2} $$

Answer:

\( \frac{5}{2} \) (the fourth option)