8.9
The Standard
The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students locate where two linear graphs intersect and name that point as an ordered pair. They substitute the x and y values into both equations to confirm the point works.
What Mastery Looks Like
- Given two graphed lines, students accurately read the intersection as an ordered pair. They substitute the coordinates into both equations and show that both equations are true.
Common Misconceptions
- Students may reverse the x and y coordinates or misread the graph’s scale. Some choose a point that lies on only one line. Others check the ordered pair in just one equation.
How to Assess It
- Exit ticket: Graph y = 2x + 1 and y = -x + 7, name the intersection, and verify the point in both equations.
Lesson moves
Ways to Teach It
Graph one equation on each transparent coordinate grid, overlay the grids, mark the intersection, and substitute its coordinates into both equations.
Write a response to: Why must the intersection point make both equations true, not just one?
Play a card match using pairs of equations, graph cards, intersection cards, and verification cards.
Graph two taxi fare rules, find when the costs match, and check that trip length in both rules.
Keep exploring
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