CCSS.Math.Content.HSA-REI.D.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, often forming a curve (which could be a line).
Common Core State Standards for Mathematics
What this standard means
Students need to connect an equation with two variables to its graph. They should understand that every point on the graph makes the equation true, and every ordered pair that makes the equation true belongs on the graph. They should test points by substitution, not just by looking.
Mastery looks like explaining why a point is or is not on a line or curve, using the equation as evidence. Students often think the graph is just a picture made from a table, or that nearby points count. They also mix up x and y when checking ordered pairs.
Ways to teach it
- Have students use sticky dots to plot only ordered pairs that satisfy y = 2x + 1, then compare the pattern to the line.
- Ask students to write: How can you prove that (3, 7) is on the graph of y = 2x + 1?
- Give three points and one equation, then ask students to circle all points that are solutions and show substitution work.
- Use a phone plan equation, cost = 20 + 15g, and ask which graph points represent possible monthly bills.
Plan a lesson for CCSS.Math.Content.HSA-REI.D.10
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSA-CED.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- CCSS.Math.Content.HSA-REI.C.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- CCSS.Math.Content.8.EE.C.8a
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...
- CCSS.Math.Content.HSA-REI.D.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 ...