Line Craft Worksheet
Math 8 • Indiana IAS 8.AF.1–3 Direct Variation & Slope
Lesson 2-6/2-7 Review
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Slope: \( m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \)
Direct Variation: \( y = kx \) or \( y = mx \) (always passes through the origin \((0, 0)\))
1 Part 1: Slope from Two Points
Apply the slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Show full substitution and steps.
#1 \((2, 5)\) and \((6, 13)\) \( (x_1, y_1) \quad (x_2, y_2) \)
Show substitution & work:
Slope \(m\) =
#2 \((-3, 8)\) and \((1, -4)\) \( (x_1, y_1) \quad (x_2, y_2) \)
Show substitution & work:
Slope \(m\) =
2 Part 2: Rate of Change from Tables
Determine \(\Delta x\), \(\Delta y\), and write the direct variation equation.
#3 Direct Variation Table
Change in \(y\) (\(\Delta y\)):
Change in \(x\) (\(\Delta x\)):
Slope \(m\):
Equation (\(y = mx\)):
#4 Varying Intervals
Two points chosen:
Ratio \(\frac{\Delta y}{\Delta x}\):
Slope \(m\):
Equation (\(y = mx\)):
3 Part 3: Slope from Graphs Through the Origin
Both lines pass through \((0, 0)\). Find rise, run, slope, and write \(y = mx\).
x y
#5 Graph A
Points: \((0, 0)\) and \((2, 3)\)
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope \(m\):
Equation:
x y
#6 Graph B
Points: \((0, 0)\) and \((1, -2)\)
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope \(m\):
Equation:
4 Part 4: Graphing Direct Variation Equations
Plot \((0, 0)\), use the slope to plot at least 2 more points, and draw the line.
x y
#7 Graph: \( y = 2x \)
Slope \(m = \frac{\text{rise}}{\text{run}}\):
Initial Point: \((0, 0)\)
2nd Point:
3rd Point:
Plot all 3 points & connect with a ruler.
x y
#8 Graph: \( y = -\frac{1}{2}x \)
Slope \(m = \frac{\text{rise}}{\text{run}}\):
Initial Point: \((0, 0)\)
2nd Point:
3rd Point:
Plot all 3 points & connect with a ruler.
Standard: IAS 8.AF.1 (Slope formula), 8.AF.2 (Rate of change), 8.AF.3 (Graph proportional/linear relationships) Single Page Handout
