Slope Sprint Worksheet
Algebra 1 Practice Linear Functions
Slope Sprint: Graphing \(y = mx\)
Graph lines through the origin using slope as rate of change (Rise over Run).
Name:
Date:
Period:
Score: / 10
Core Rule for \(y = mx\)
Since there is no added constant (\(b = 0\)), every line passes through the Origin \((0,0)\).
Step 1: Plot point at \((0,0)\)
Step 2: Slope \(m = \frac{\text{Rise}}{\text{Run}}\) \(+\) Up / \(-\) Down • Run Right
Step 3: Connect with ruler & arrows
Part 1: Guided Graphing (Problems 1 – 4)
Find slope, list rise/run, plot 2 points, draw the line
Problem 1 \(y = 2x\)
x y 2 4 -2 2 4 -2
Slope (\(m\)):
Fraction form:
• Rise: (Up/Down)
• Run: (Right)
Two Points:
Pt 1: (0, 0)
Pt 2: ( , )
Problem 2 \(y = \frac{1}{3}x\)
x y 2 4 -2 2 4 -2
Slope (\(m\)):
Direction:
• Rise: (Up/Down)
• Run: (Right)
Two Points:
Pt 1: (0, 0)
Pt 2: ( , )
Problem 3 \(y = -3x\)
x y 2 4 -2 2 4 -2
Slope (\(m\)):
↓ Negative = Fall down!
• Rise: (Down)
• Run: (Right)
Two Points:
Pt 1: (0, 0)
Pt 2: ( , )
Problem 4 \(y = -\frac{3}{4}x\)
x y 2 4 -2 2 4 -2
Slope (\(m\)):
Fraction slope
• Rise: (Down)
• Run: (Right)
Two Points:
Pt 1: (0, 0)
Pt 2: ( , )
Always draw arrows at both ends of your line to show it extends indefinitely! Page 1 of 2
Slope Sprint Graphing \(y = mx\) • Independent Practice & Analysis
Name:
Part 2: Independent Practice (Problems 5 – 8)
Watch signs and improper fractions carefully
Problem 5 \(y = \frac{4}{3}x\)
x y
Slope (\(m\)):
Rise: • Run:
Pt 1: (0, 0)
Pt 2: ( , )
Problem 6 \(y = -x\)
x y
Slope (\(m\)):
Rise: • Run:
Pt 1: (0, 0)
Pt 2: ( , )
Problem 7 \(y = \frac{1}{2}x\)
x y
Slope (\(m\)):
Rise: • Run:
Pt 1: (0, 0)
Pt 2: ( , )
Problem 8 \(y = -\frac{2}{3}x\)
x y
Slope (\(m\)):
Rise: • Run:
Pt 1: (0, 0)
Pt 2: ( , )
Part 3: Slope Sleuth (Thinking Deeper)
Conceptual reasoning and reversing the process
Problem 9 Steepness Comparison
Two students graph lines that pass through \((0,0)\): Line A has the equation \(y = 4x\) and Line B has the equation \(y = \frac{1}{4}x\).
a) Which line is steeper? Explain using the relationship between rise and run:
b) What would happen to the direction of Line A if the equation were changed to \(y = -4x\)?
Problem 10 Work Backwards: Find the Equation
A line passes through the origin \((0,0)\) and the point \((5, -2)\).
1. Find the slope:
\(m = \frac{\Delta y}{\Delta x} = \frac{\text{Change in } y}{\text{Change in } x} = \)
2. Write the equation in \(y = mx\) form:
\(y =\) \(x\)
Double-check: Did your negative slope lines go down from left to right? Page 2 of 2
Slope Sprint Answer Key
Answer Key & Guide Algebra 1 • Linear Functions
Slope Sprint: Graphing \(y = mx\)
Teacher Reference • Solutions & Common Student Misconceptions
Grading Key
Total Points: 10 pts
1 pt per problem (1–10)
Quick Spot-Check Guide
Every line must pass directly through \((0,0)\). Check that positive slopes go UP from left-to-right, and negative slopes go DOWN.
Common Error: Confusing \(\frac{\text{Rise}}{\text{Run}}\) as \(\frac{\text{Run}}{\text{Rise}}\).
Remind students: "Y rises to the sky, X runs across."
Part 1 Solutions: Guided Graphing (Problems 1 – 4)
Red lines show correct plotted graphs & points
Problem 1 \(y = 2x\)
x y
Slope (\(m\)): 2
Fraction form: \(\frac{2}{1}\)
• Rise: 2 (Up 2)
• Run: 1 (Right 1)
Sample Points:
Pt 1: (0, 0)
Pt 2: (1, 2) or (2, 4)
Problem 2 \(y = \frac{1}{3}x\)
x y
Slope (\(m\)): \(\frac{1}{3}\)
Direction: Positive (↗)
• Rise: 1 (Up 1)
• Run: 3 (Right 3)
Sample Points:
Pt 1: (0, 0)
Pt 2: (3, 1) or (6, 2)
Problem 3 \(y = -3x\)
x y
Slope (\(m\)): -3
Fraction: \(-\frac{3}{1}\)
• Rise: -3 (Down 3)
• Run: 1 (Right 1)
Sample Points:
Pt 1: (0, 0)
Pt 2: (1, -3) or (-1, 3)
Problem 4 \(y = -\frac{3}{4}x\)
x y
Slope (\(m\)): \(-\frac{3}{4}\)
Direction: Negative (↘)
• Rise: -3 (Down 3)
• Run: 4 (Right 4)
Sample Points:
Pt 1: (0, 0)
Pt 2: (4, -3) or (-4, 3)
Award 0.5 pt for accurate slope identification and 0.5 pt for correct graphed line through (0,0). Page 1 of 2
