7.7
The Standard
The student applies mathematical process standards to represent linear relationships using multiple representations. The student is expected to represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students translate a linear relationship among a verbal description, table, graph, and equation. They identify the constant rate of change and starting value, then write an equation in y = mx + b form.
What Mastery Looks Like
- Given one representation, students can create the other three. They can check that table pairs and graph points satisfy the equation, then explain the rate and starting value in context.
Common Misconceptions
- Students often swap the rate of change and the starting value. They may treat the first table value as the starting value even when x is not zero. They may ignore graph scales or calculate slope backward.
How to Assess It
- Give the table x: 0, 2, 4 and y: 3, 7, 11. Ask students to write an equation, plot the points, and describe the relationship in words.
Lesson moves
Ways to Teach It
Stack identical cups, measure height after each cup, then build a table, graph, and equation from the measurements.
Write and discuss: In y = 4x + 7, what do 4 and 7 mean in a phone-charging situation?
Match cards showing verbal descriptions, tables, graphs, and equations, then justify each set by naming the same rate and starting value.
Model a taxi fare with a starting fee and per-mile charge, then represent the cost using words, a table, graph, and equation.
Keep exploring
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