Lesson 4: Graphing Across All Four Quadrants
Duration of Days: 2
Lesson Objective
Students will be able to graph linear equations in slope-intercept form (y=mx+b) across all four quadrants of the coordinate plane, accurately plotting the y-intercept and using positive, negative, and fractional slopes to map consecutive coordinates.
How do the signs of the coordinates in each quadrant change the way we plot points for a linear equation?
If a line crosses from Quadrant III to Quadrant I, what does that tell us about its slope and y-intercept?
How does a negative slope affect the direction you move ("rise" and "run") across different quadrants?
Quadrants (I, II, III, IV)
Origin (0,0)
Coordinate Plane / Cartesian Grid
Ordered Pair (x,y)
x-axis / y-axis
y-intercept (b)
Slope (m)
8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
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.
Description: This lesson extends students' graphing skills from the first quadrant into a full four-quadrant coordinate plane.
Purpose: To build spatial and structural math fluency, ensuring students understand that linear relationships exist continuously across all coordinate spaces, not just positive values.
DOK Level: Level 2 (Basic Application of Skills & Concepts).
Quadrant Confusion: Students mislabeling the Roman numerals or order of the quadrants (counter-clockwise starting from the top right).
Sign Rules for Slope: Confusing a negative coordinate location with a negative slope.
Directional Errors: Moving the wrong way along the y-axis when plotting a negative y-intercept.
Provide graphic organizers labeled with the (+,+) signs for each quadrant.
Student work
Exit Ticket