Story Equations
About This Worksheet
This worksheet helps eighth-grade students match linear equations with the real-world situations they represent. Students compare equations with stories involving bike rentals, travel distance, savings, plant growth, delivery charges, worker pay, taxi rides, and temperature changes. They must use both the slope and the y-intercept to decide which situation fits each equation. This makes the activity a strong review of how linear models are built from a starting amount and a constant rate of change. It also helps students see that equations can describe many different kinds of everyday relationships.
What Students Practice
Students identify the slope and y-intercept in each equation and compare those values with the rates and starting amounts described in the situations. They determine whether a relationship begins with a fixed fee, starting balance, initial height, or another value, and whether it increases or decreases over time. Some equations have positive rates while others have negative rates. This gives students practice with equation structure, real-world modeling, units, and interpretation. The matching format encourages them to use both pieces of information instead of relying on only one clue.
Why This Matters
A linear equation tells a complete story when students understand what m and b represent. Matching equations to situations helps them see that the slope describes a rate and the y-intercept describes where the situation begins. This is an important modeling skill because students will often need to write equations from verbal descriptions later. It also strengthens their ability to compare linear relationships across equations, graphs, and contexts. Understanding these connections is central to Grade 8 function work.
Teaching Tips
Have students underline the rate in each story and circle the starting amount. Then compare those values with the slope and y-intercept in the equations. If two situations seem similar, check both pieces of information before making the match. Encourage students to read each equation aloud as a sentence, such as “starts at 60 and increases by 25 each time.” This makes the relationship easier to connect with the correct story.
Curriculum Standards
This worksheet strongly supports CCSS.MATH.CONTENT.8.F.B.4 by asking students to model and interpret linear relationships using slope and initial value. It also supports CCSS.MATH.CONTENT.8.F.A.2 by strengthening students’ ability to compare function features across different representations. The real-world matching format helps connect symbolic equations with verbal descriptions. It works well for independent practice, homework, review, or cumulative assessment.