Georgia 8.PAR.4.2
The Standard
Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane.
Georgia's K-12 Mathematics Standards · Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students connect an equation, its ordered-pair solutions, and its graph. They test coordinate pairs, plot the pairs that make the equation true, and explain what the points mean in context.
What Mastery Looks Like
- Students can test an ordered pair by substituting both values into the equation. They can plot valid pairs and explain why points on the graph work while points off the graph do not.
Common Misconceptions
- Students may think any point near the line is a solution. They may reverse the coordinates, ignore the axis labels, or plot only a few tested pairs without recognizing the other solutions.
How to Assess It
- Give students y = 3x + 2 and the points (2, 8), (2, 7), and (0, 2). Ask them to identify which points belong on the graph and justify each choice by substitution.
Lesson moves
Ways to Teach It
Give pairs of students coordinate cards for y = 2x + 1; they test, then place valid cards on a floor grid.
Ask, "Why does (4, 11) belong on the graph of c = 2n + 3, while (4, 10) does not?"
Play Graph Detective: teams use substitution to sort point cards into on the graph and off the graph, then justify one choice.
Model a taxi fare with f = 3m + 5, plot several solutions, and explain what each coordinate means for a rider.
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