Procedure: Graphing y = mx using the Origin and Slope
Graphing y = mx in 8th grade starts at the origin (0, 0) because all proportional relationships pass through the origin. From the origin, use slope m as rise over run to find a second point. For y = 3x: slope = 3/1, so rise 3 and run 1 to reach (1, 3), then draw the line. For y = -2/5 x: go down 2 and right 5 to reach (5, -2). This procedure from enVision Mathematics, Grade 8, Chapter 2 gives students a reliable two-point graphing method for all linear proportional relationships.
Key Concepts
To graph a linear equation of the form $y = mx$: 1. Start by plotting a point at the origin, $(0, 0)$. 2. From the origin, use the slope $m = \frac{\text{rise}}{\text{run}}$ to find a second point. 3. Draw a straight line that passes through both the origin and the second point.
Common Questions
How do I graph y = mx?
Start at the origin (0, 0). Use the slope m as rise over run to find a second point. Draw a straight line through both points.
Why does y = mx always pass through the origin?
When x = 0, y = m times 0 = 0. The origin (0, 0) satisfies any equation of the form y = mx, so all these graphs pass through it.
Graph y = 4x using slope from origin.
Start at (0, 0). Slope = 4/1: rise 4, run 1. Second point: (1, 4). Draw line through (0,0) and (1, 4).
Graph y = -3/4 x.
Start at (0, 0). Slope = -3/4: go down 3 and right 4. Second point: (4, -3). Draw line through (0, 0) and (4, -3).
How is y = mx different from y = mx + b?
y = mx passes through the origin (initial value is 0). y = mx + b passes through (0, b) where b is the y-intercept.
When do 8th graders learn to graph y = mx?
Chapter 2 of enVision Mathematics, Grade 8 covers this in the Analyze and Solve Linear Equations unit.