Determine and interpret the slope (rate of change) and y-intercept (starting value).
Explain similarities and differences between functions in multiple representations.
Apply comparisons of linear functions to real-world contexts like budgeting, travel, and data analysis.
Strengthen reasoning skills aligned with Common Core Standards 8.F.A.2 and 8.F.A.3.
Many students freeze when they see different forms of linear functions graphs, tables, equations, or word problems. This worksheet removes that confusion by teaching how to compare functions step by step, using multiple methods.
By exploring slope (rate of change) and intercept (starting value), learners build confidence and develop strong reasoning skills.
A linear function shows a constant rate of change. To compare functions, we look at how steeply they rise (slope) and where they start (y-intercept).
For example:
y = 2x + 3 and y = 2x + 5 have the same slope but different intercepts.
Historically, functions were compared using hand-drawn graphs and tables. Today, technology and visuals make it much easier for students to see and analyze relationships in different ways.
Problem:
Table A:
| x | y |
|---|---|
| 0 | 2 |
| 1 | 5 |
| 2 | 8 |
Equation B: y = 3x
Solution:
From the table, y increases by +3 each time → slope = 3
Equation B also has slope = 3
Both grow at the same rate, but Table A starts higher (y-intercept = 2).
 Answer: Same slope, but Table A starts higher.
Comparing linear functions is not just a classroom skill—it’s a life skill. Whether choosing the cheaper taxi, comparing mobile plans, or analyzing savings, students need to identify which function grows faster or starts higher.
Aligned with 8.F.A.2 and 8.F.A.3, this worksheet gives practice in comparing:
Equations
Graphs
Tables
Word problems
Identify the Representation – Is it a table, graph, or equation?
Find the Rate of Change (Slope) – How fast does y change compared to x?
Find the Starting Point (Intercept) – Where does it begin?
Compare Functions – Which grows faster or starts higher?
Apply in Real Life – Use the comparison to answer real-world problems.
How to Compare Linear Functions
Example 1 (Equation vs. Equation):
Compare y = 2x + 1 and y = 3x + 1
 Slopes: 2 vs. 3
Second grows faster.
Example 2 (Word Problem):
Ali’s taxi charges 50 + 10x, Bilal’s charges 5x.
 Slopes: 10 vs. 5
Bilal’s grows slower, but he has no starting fee.
Budgeting: Comparing income growth
Transportation: Cheaper ride vs. faster ride
Business: Which company grows sales faster?
Sports: Which athlete’s performance improves quicker?
"Before, I couldn’t tell which graph was better. Now I can compare instantly!" – Aisha, 8th Grade Student
"These worksheet at NumericWiz.com connects equations, graphs, and tables in one place. My students gained real confidence." – Mr. Khan, Math Teacher
Download the worksheet, solve it, and upload your answers on our Evaluate Your Work page. Teachers will check and send you personalized feedback.
Keep practicing with the worksheet.
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