Energy Use: Comparing Algebraic and Graphical Representation
Help students master comparing linear functions represented in different ways with this real-world, standards-aligned worksheet. In this activity, students compare algebraic equations and graphs to analyze how energy usage changes over time in two public buildings.
Rather than working with abstract lines and numbers, students apply math to authentic energy monitoring scenarios, making slope and y-intercept meaningful and memorable.
Short Storyline (Student Context)
A city is monitoring energy usage in two public buildings.
- Building A follows an engineering model that predicts energy use using an algebraic function.
- Building B uses sensor data displayed on a graph to track real usage.
Throughout the day, energy usage changes during the morning, afternoon peak hours, and overnight. Students act as city analysts, comparing the two buildings to determine which uses energy faster and why.
What Students Will Do
Across three interconnected sections, students will:
- Compare two different linear functions
- Interpret one function from an equation
- Interpret another function from a graph
- Identify y-intercepts (starting energy use)
- Identify slopes (rate of energy change)
- Compare positive and negative rates of change
- Predict energy usage after a given number of hours
- Justify conclusions using numerical evidence
Scenarios Included
- Morning energy usage as buildings power up
- Afternoon peak hours with full system operation
- Overnight energy use as systems shut down
Each scenario reinforces the same comparison skills while varying the context and rates.
Skills & Standards Covered
- Compare properties of two linear functions
- Interpret slope and y-intercept from algebraic and graphical representations
- Analyze increasing and decreasing linear functions
- Extend linear patterns to make predictions
- Communicate mathematical reasoning
Aligned to CCSS: 8.F.A.2
Why Teachers Love This Worksheet
- Strong focus on representation comparison (equation vs graph)
- Clear real-world purpose for every scenario
- Builds conceptual understanding of slope vs intercept
- Includes both positive and negative slopes
- Structured, repeatable format supports student confidence
- Works well for classwork, homework, or assessment
- Supports randomization, giving each student unique equations and graphs
Learning Objective
Students will compare two linear functions represented algebraically and graphically by identifying and interpreting rate of change (slope) and initial value (y-intercept), and determine which function increases or decreases faster in real-world energy usage scenarios.
Randomization Available
This worksheet supports randomization, meaning each student receives different y-intercepts and slopes for the algebraic equations and graphs. This encourages independent reasoning and prevents 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.
