NY Next Generation Math AI-A.REI.10
The Standard
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students connect an equation in two variables with every coordinate pair that makes it true. In Algebra I, they graph those pairs and use the graph as the equation's complete solution set.
What Mastery Looks Like
- The student tests points by substitution and explains why points on the graph are solutions while off-graph points are not. The student can generate and graph additional solutions accurately.
Common Misconceptions
- Students may treat one point as the entire solution or assume every plotted point is valid. They may graph an expression without recognizing the coordinates as satisfying pairs.
How to Assess It
- Give 2x plus y equals 6 and the points (1,4), (2,1), and (4,-2). Ask students to test each and explain its graph location.
Lesson moves
Ways to Teach It
Plot coordinate cards after substituting each pair into an equation, using different colors for solutions and nonsolutions.
Ask students why a continuous line represents infinitely many solutions rather than only the visible grid points.
Play graph detective by matching equations, solution tables, and graphs.
Graph combinations of two ticket types that produce a fixed event revenue and interpret several solution points.
Keep exploring
Related Standards
- AII-A.REI.7.b
Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- AI-A.REI.12
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution ...
- AI-A.REI.6.a
Solve systems of linear equations in two variables both algebraically and graphically.
- NY-8.EE.8.a
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersect...
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