Georgia 8.FGR.7.3
The Standard
Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection
Georgia's K-12 Mathematics Standards · Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students graph two linear equations on the same coordinate plane and estimate where the lines intersect. They also identify simple solutions by inspecting the equations or graphs.
What Mastery Looks Like
- Students graph both equations accurately and identify the intersection as the shared solution. They estimate noninteger coordinates from the scale and recognize simple systems that can be solved by inspection.
Common Misconceptions
- Students may treat any point on either line as a solution instead of finding the intersection. They may reverse coordinates, misread graph scales, or report an exact answer when the graph supports only an estimate.
How to Assess It
- Give students a graph of two intersecting lines and ask, "Estimate the solution, then explain how the graph shows your answer satisfies both equations."
Lesson moves
Ways to Teach It
Graph two equations on separate transparent grids, overlay them, and mark the intersection with its estimated coordinates.
Ask students to explain why the intersection solves both equations and how graph scale affects the accuracy of their estimate.
Play Intersection Match by pairing equation cards with graph cards and solution cards, including parallel and identical lines.
Compare two phone plans by graphing total monthly cost against data use, then estimate when both plans cost the same.
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Printable 8.FGR.7.3 Worksheet
A ready-to-print activity worksheet aligned to 8.FGR.7.3, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 8.FGR.7.2
Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of...
- 8.PAR.4.2
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 p...
- 8.FGR.7.4
Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.
- 8.FGR.7.1
Interpret and solve relevant mathematical problems leading to two linear equations in two variables.
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