MathematicsFreePrintable
Graphing Proportional Relationships
A free mathematics worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.
Graphing Proportional Relationships
📊 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?
✏️ Part 3: Reasoning and Justification
9. Explain why the constant of proportionality (k in y = kx) represents the unit rate of change. Use an example to support your explanation.
10. How can you tell if two points represent a proportional relationship? Check all methods that apply:
Both points lie on a line that passes through the origin (0,0)
The ratio y/x is the same for both points
The points have the same x-coordinate
The equation y = kx works for both points with the same value of k
11. Given the points (2, 6) and (4, 12), determine if they represent a proportional relationship. Justify your answer with calculations.
About This Worksheet
Free in Kuraplan
Sign up free, grab the PDF, and customize it for your class.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free No credit card Curriculum-aligned Under 60 seconds
