Lesson 3: Converting Between Forms (Ax+By=C to y=mx+b)
Duration of Days: 1
Lesson Objective
Students will be able to algebraically manipulate linear equations to convert fluidly between Standard Form (Ax+By=C) and Slope-Intercept Form (y=mx+b), isolating variables to identify slope and intercepts.
How do the algebraic properties of equality allow us to rewrite an equation without changing the line it represents on a graph?
Why is isolating y necessary to reveal the slope and y-intercept of a line written in standard form?
What are the common algebraic pitfalls when moving terms or dividing by negative coefficients?
Standard Form (Ax+By=C)
Slope-Intercept Form (y=mx+b)
Literal Equation / Variable Isolation
Properties of Equality
Inverse Operations
Coefficient & Constant
CCSS.MATH.CONTENT.8.EE.C.7: Solve linear equations in one variable.
CCSS.MATH.CONTENT.8.EE.C.7.B: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Description: This lesson focuses on the algebraic mechanics of literal equations.
Purpose: To bridge structural representations of lines, allowing students to verify their visual graphing strategies (from Day 2) using traditional slope-intercept tools.
DOK Level: Level 2 (Basic Application of Skills & Concepts)
When subtracting Ax from both sides, students frequently combine it with the constant C (e.g., simplifying 12-3x to 9x).
Dropping negative signs during division
Utilize a color-coded "two-step" graphic organizer template.
Exit ticket