Lesson 2: Graphing from Standard Form & Writing Equations
Duration of Days: 1
Lesson Objective
Students will be able to efficiently graph linear equations from standard form (Ax+By=C) by finding and plotting the x- and y-intercepts, and write standard form equations to represent real-world combinations of two quantities.
How does plotting both intercepts give us enough information to graph a complete line?
In what scenarios is it more efficient to graph using intercepts rather than converting to slope-intercept form (y=mx+b)?
How do the coefficients (A and B) and the constant (C) relate to the rate and total constraints in a word problem?
Standard Form (Ax+By=C)
Intercepts (X-intercept / Y-intercept)
Slope-Intercept Form (y=mx+b)
Coefficients
Constant / Constraints
Linear Graphing
CCSS.MATH.CONTENT.8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph.
CCSS.MATH.CONTENT.8.EE.C.7: Solve linear equations in one variable.
Description: This lesson transitions students from purely calculating intercepts to utilizing them as a rapid graphing strategy.
Purpose: To master graphing without relying on rewriting equations, and to build the foundational skills needed to interpret linear constraints in real-world models.
DOK Level: Level 2 (Basic Application of Skills & Concepts)
Students may graph the intercepts on the wrong axes (e.g., putting the value found for the x-intercept onto the y-axis).
When writing equations from word problems, students might incorrectly match the coefficients with the wrong variables.
Forgetting that a line cannot be graphed using this method if it passes through the origin (C=0), as both intercepts will yield the single point (0,0).
Provide a step-by-step checklist card: (1) Find x-intercept, (2) Plot on x-axis, (3) Find y-intercept, (4) Plot on y-axis, (5) Connect with a ruler.
Use pre-labeled coordinate grids.
Task Cards
Exit Ticket