Slope Mastery Practice Sheet
Grade 10 Mathematics • Analytic Geometry
Slope Mastery Practice Sheet
Finding slope from graphed lines, coordinates, and linear forms
Name:
Date: Per:
Rise over Run
\( m = \frac{\Delta y}{\Delta x} = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1} \)
Horizontal & Vertical
Horizontal: \( m = 0 \)
Vertical: \( m = \text{undefined} \)
Parallel & Perpendicular
Parallel: \( m_1 = m_2 \)
Perpendicular: \( m_1 \cdot m_2 = -1 \)
1
Find the Slope of Each Graphed Line
Count rise and run between highlighted lattice points.
x y
Graph A
Point 1:
Point 2:
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope \( m = \)
x y
Graph B
Point 1:
Point 2:
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope \( m = \)
x y
Graph C
Point 1:
Point 2:
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope \( m = \)
x y
Graph D
Point 1:
Point 2:
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope \( m = \)
2
Algebraic Slope Calculations
Apply formula or convert to \( y = mx + b \).
Problem 5: Coordinate Formula
Points: \( P(-4, 7) \) and \( Q(6, -8) \)
Slope \( m = \)
Problem 6: Standard Form Equation
Linear Equation: \( 4x - 6y = 18 \)
Slope \( m = \)
Unit 3: Coordinate Geometry & Analytic Proofs Page 1 of 2
Slope Mastery Practice Sheet • Part II: Geometric Applications
Name:
3
Graphed Lines: Parallel & Perpendicular Criteria
Find both slopes from the graph and classify the relationship.
L₁ L₂
Pair A: Compare Lines
Slope \( L_1 \):
Slope \( L_2 \):
Classification:
Parallel Perp. Neither
L₃ L₄
Pair B: Compare Lines
Slope \( L_3 \):
Slope \( L_4 \):
Classification:
Parallel Perp. Neither
4
Coordinate Proof: Right Triangle Verification
Problem 9: Given vertices \( A(-2, 3) \), \( B(2, 6) \), and \( C(5, 2) \).
Compute the slopes of segments \( \overline{AB} \), \( \overline{BC} \), and \( \overline{AC} \). Determine whether \( \Delta ABC \) contains a right angle.
Slope of \( \overline{AB} \):
\( m_{AB} = \)
Slope of \( \overline{BC} \):
\( m_{BC} = \)
Slope of \( \overline{AC} \):
\( m_{AC} = \)
Geometric Conclusion (Are any two sides perpendicular?):
5
Contextual Rate of Change & Error Analysis
Problem 10: Drone Descent Rate
A drone descends from \( 480\text{ m} \) after \( 4\text{ seconds} \) to \( 120\text{ m} \) after \( 16\text{ seconds} \).
Calculated Slope:
Units & Meaning:
Problem 11: Spot and Correct the Error
Points: \( (-2, 5) \) and \( (4, -7) \)
Student writes: \( m = \frac{4 - (-2)}{-7 - 5} = \frac{6}{-12} = -\frac{1}{2} \)
Correct Slope:
Unit 3: Coordinate Geometry & Analytic Proofs Page 2 of 2
