Lesson 1: Solving and Analyze Systems by Graphing
Duration of Days: 3
Lesson Objective
Graph pairs of linear equations on a coordinate plane to locate and estimate their point of intersection (x,y) as a solution.
Identify whether a system has one solution, no solution (parallel lines), or infinitely many solution.
How does the coordinate point (x,y) where two lines intersect mathematically satisfy both linear equations at the exact same time?
What structural clues in a system of equations (like slope and y-intercept) can instantly tell us if the lines will cross once, never cross, or sit directly on top of each other?
If two linear equations have the exact same slope but different y-intercepts, what does their graph look like, and how many solutions exist?
System of linear equations, Point of intersection, Simultaneous solution, Ordered pair, Unique solution, Parallel lines, No solution, Coinciding lines, Infinitely many solutions, Inspection, Slope-intercept form.
CCSS.MATH.CONTENT.8.EE.C.8.A, CCSS.MATH.CONTENT.8.EE.C.8.B
Description/Purpose: Students bridge their past knowledge of graphing single lines to analyzing pairs of lines simultaneously. Students use "inspection" to predict the number of solutions (one, none, or infinite) based entirely on comparing slopes and intercepts.
DOK Level: 2 (Skill/Concept Application) & 3 (Strategic Thinking / Structural Analysis)
The Scale Error: Missing the exact intersection point because lines were sketched carelessly.
Students frequently mix up parallel lines (different intercepts = no solution) with coinciding lines (same intercept = infinitely many solutions).
Provide pre-printed coordinate grids with the lines faintly dashed to assist with graphing accuracy.
Exit Tickets