Lesson 1: Introduction to Slope-Intercept Form
Duration of Days: 2
Lesson Objective
Students will be able to identify the slope (m) and y-intercept (b) from a linear equation written in slope-intercept form and explain the structural placement and mathematical purpose of each variable within the formula y=mx+b.
What do the variables m and b represent in the equation y=mx+b?
Why does the slope always sit next to the independent variable (x) while the y-intercept stands alone?
How can you tell if a line will tilt upward or downward just by looking at its equation?
Slope (m) / Rate of Change
y-intercept (b) / Initial Value
Linear Equation
Variable
Constant
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.B.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mx for a line through the origin and the equation y=mx+b for a line intercepting the vertical axis at b
This introductory lesson transitions students from simple proportional relationships (y=mx) to full linear relationships (y=mx+b). It establishes the algebraic framework necessary for the rest of the unit.
DOK Level: DOK 1 (Recall and Recognition of equation parts) transitioning to DOK 2 (Basic Application of identifying parts in non-standard arrangements).
Students frequently switch the positions of m and b, assuming the first number is always the slope (e.g., in y=4+2x, misidentifying 4 as the slope).
Students often include the x variable when identifying the slope (e.g., stating the slope is "2x" instead of just "2").
Confusion regarding operations as signs (e.g., not realizing that in y=3x-5, the y-intercept is -5).
Support (Scaffolding): Provide a color-coded graphic organizer where m is always highlighted in one color and b in another.
Exit Ticket