Graphing Proportional Relationships

Name:

Date:

Graph with proportional relationship line

📊 Part 1: Understanding Proportional Relationships

1. A proportional relationship can be written as y = kx, where k is the constant of proportionality. Which of the following represents a proportional relationship?

y = 3x + 2

y = 5x

y = x - 1

y = 2x + 4

2. Priya jogs at a constant speed. In 2 hours, she travels 8 miles. What is the constant of proportionality (unit rate) for distance traveled per hour?

2 miles per hour

4 miles per hour

8 miles per hour

16 miles per hour

3. Complete the table for the proportional relationship y = 3x:

x: 0, 1, 2, _____, 4
y: 0, _____, 6, 9, _____

4. A you-pick blueberry farm sells 5 pounds of blueberries for $24. Write an equation for the cost (c) based on pounds (p) purchased.

Equation: c = _______ × p

📈 Part 2: Graphing and Analysis

5. Use the blueberry farm equation from question 4. Create a table and graph the relationship on the coordinate plane below.

6. What is the cost for 8 pounds of blueberries? Show your work.

7. Error Analysis: A student claims that the point (3, 11) lies on the line y = 4x. Identify and explain the error.

Step 1: Substitute x = 3 into the equation: y = 4(___) = _____

Step 2: Compare with the given point (3, 11):

8. Two bugs are moving at constant speeds. Bug A travels according to y = 2x and Bug B travels according to y = 5x, where x is time in seconds and y is distance in inches. Which bug moves faster and why?