Comparing Linear Models: Which Changes Faster?
This interactive worksheet helps students deepen their understanding of linear relationships by comparing real-world situations using graphs and equations. Instead of focusing only on calculations, students analyze how slope and y-intercept affect decisions, making this activity ideal for building conceptual understanding and real-life application skills.
Students explore two realistic scenarios where linear models are used to predict costs and compare options. By identifying rates of change and starting values from graphs, learners write equations in slope-intercept form and use them to determine which option is better under different conditions.
What students will do
- Read and interpret linear graphs
- Identify the y-intercept as the starting value
- Identify the slope as the rate of change
- Write equations in the form y= mx + b
- Use equations to predict values beyond the graph
- Compare linear models to make informed decisions
Real-World Scenarios Included
- Internet Plan Comparison
- Students compare two internet plans with different base fees and data usage rates to determine which plan is better for low and high data usage.
- Taxi Ride Comparison
- Students analyze two taxi services with different base fares and per-mile charges to decide which option is more cost-effective for short and long trips.
Why teachers will love this worksheet
- Strong real-world connections that engage students
- Emphasis on reasoning and comparison, not just computation
- Encourages multiple valid methods for finding slope
- Supports randomization, giving each student different slopes and intercepts
- Perfect for classwork, homework, or formative assessment
This worksheet is an excellent next step after introducing slope-intercept form, helping students see how linear equations are powerful tools for prediction and decision-making in everyday situations.
Learning Objective
Students will analyze and compare linear relationships by identifying slope and y-intercept from graphs, writing equations in slope-intercept form, and using those equations to predict and evaluate real-world outcomes.
Randomization Available
This worksheet supports randomization. When enabled, each student will receive different slopes and y-intercepts for each plan, resulting in unique equations, tables, and predictions. This helps promote independent thinking and reduces copying.
💡 Tip: When assigning this activity to your classroom, you can optionally enable randomization to give each student a unique version of the problems. When you re-assign the same worksheet, each student will get a new set of questions, helping them master the content through repeated practice.
