Question

1. for each diagram, decide if y is an increase or a decrease relative to x. then determine the percent increase or decrease.

Explanation:

Part A

Step1: Analyze the length of x and y

From the diagram, \( x \) is represented by 4 equal parts, and \( y \) is represented by 3 equal parts. So \( y < x \), which means it's a decrease.

Step2: Calculate the percent decrease

The formula for percent decrease is \( \frac{x - y}{x} \times 100\% \). Here, \( x = 4 \) parts, \( y = 3 \) parts. So \( \frac{4 - 3}{4} \times 100\%=\frac{1}{4} \times 100\% = 25\% \).

Part B

Step1: Analyze the length of x and y

From the diagram, \( x \) is represented by 4 equal parts, and \( y \) is represented by 5 equal parts. So \( y > x \), which means it's an increase.

Step2: Calculate the percent increase

The formula for percent increase is \( \frac{y - x}{x} \times 100\% \). Here, \( x = 4 \) parts, \( y = 5 \) parts. So \( \frac{5 - 4}{4} \times 100\%=\frac{1}{4} \times 100\% = 25\% \).

Answer:

• Part A: Decrease, 25% decrease.
• Part B: Increase, 25% increase.