Understanding Linear Relationships and Their Graphs
Grade Level:
8th Grade
Topics:
Linear
Duration:
20-25 Mins
What you’ll learn
In this lesson, you’ll learn what linear relationships are and how they are represented using tables, graphs, and real-life situations.
Why this matters
Linear relationships describe how one quantity changes in relation to another. They are the foundation of algebra, science formulas, and everyday situations like speed, cost, and distance.
What is a linear relationship?
A linear relationship is a relationship between two variables that changes at a constant rate.
This means:
When one value increases, the other increases (or decreases) by the same amount each time
The graph of a linear relationship is a straight line
Linear relationships in real life
Examples of linear relationships:
Earning a fixed amount of money per hour
Distance traveled at a constant speed
Cost per item when the price doesn’t change
Example:If you earn $10 per hour, every additional hour adds $10 to your total earnings.
Tables and patterns
Linear relationships often appear in tables.
Notice the pattern:
Each time hours increase by 1
Earnings increase by 10
This constant change is called the rate.
Graphing linear relationships
To graph a linear relationship:
Draw a coordinate plane
Plot the points from the table
Connect the points with a straight line
The straight line shows that the relationship is linear.
Understanding slope (informal)
The slope describes how steep a line is.
A steep line means a large change
A gentle line means a smaller change
For now, think of slope as:
“How much one quantity changes when the other increases by one.”
Step-by-step example
Example: A bike rental costs $5 per hour.
Plot the points (1,5), (2,10), (3,15)
Connect them to form a straight line
The line shows a constant increase of $5 per hour. That means for every hour you rent the bike, the cost increases by $5.
Try it together (Parent + Student)
Choose a situation with a constant rate (allowance, steps per minute, pages read per day).
Make a table
Plot the points
Talk about what the graph shows
Parents: ask “What stays the same each time or remains constant?”
Independent practice
Students create tables and graphs to represent linear relationships and explain the meaning of the graph in words.
Common mistakes to avoid
❌ Connecting points that don’t follow a straight pattern
❌ Forgetting that linear means constant change
❌ Mixing up the axes when graphing
If you can explain why a graph is a straight line, you understand linear relationships.
