Slope Quest Worksheet
SLOPE QUEST
From Visual Grids to Coordinate Pairs
Name:
Date:
Period:
↗
Positive
Rises left to right
↘
Negative
Falls left to right
→
Zero Slope
Horizontal (\(m = 0\))
↑
Undefined
Vertical line
Part 1 Review: Count Rise & Run on the Coordinate Plane
Slope \(m = \frac{\text{Rise}}{\text{Run}} = \frac{\Delta y}{\Delta x}\)
(-2,-3) (2,3)
1. Find the slope:
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope (\(m\)):
(-3,2) (3,-2)
2. Find the slope:
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope (\(m\)):
(-4,2) (2,2)
3. Find the slope:
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope (\(m\)):
(3,2) (3,-3)
4. Find the slope:
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope (\(m\)):
Part 2 The Bridge: The Slope Formula
No graph paper needed!
When points are far apart, like (45, 120), graphing is inefficient. Instead, calculate the difference directly:
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Worked Model: Points (1, 3) and (4, 9)
Step 1: Label \((x_1, y_1) = (1, 3)\)
\((x_2, y_2) = (4, 9)\)
Step 2: Substitute \(m = \frac{9 - 3}{4 - 1}\)
Step 3: Simplify \(m = \frac{6}{3} = 2\)
Guided Try It Together: Label, Substitute, & Solve
5. \((2, 5)\) and \((6, 13)\) Scaffolded
1. Label: \(x_1 = \) ___, \(y_1 = \) ___ | \(x_2 = \) ___, \(y_2 = \) ___
2. Substitute: \(m = \frac{\quad - \quad}{\quad - \quad}\)
3. Simplify:
6. \((-1, 4)\) and \((3, -8)\) Watch the signs!
1. Label: \(x_1 = \) ___, \(y_1 = \) ___ | \(x_2 = \) ___, \(y_2 = \) ___
2. Substitute: \(m = \frac{\quad - \quad}{\quad - (\quad)}\)
3. Simplify:
Slope Quest • Page 1: Graphical Review & Slope Formula Intro Turn over for Extended Practice →
Page 2
Extended Practice & Mastery
Formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Part 3 Find the Slope from Given Coordinate Pairs
Simplify all fractions
7. \((3, 2)\) and \((7, 10)\) Standard
Show substitution & simplification:
\(m =\)
8. \((-2, 8)\) and \((4, -10)\) Negatives
Show substitution & simplification:
\(m =\)
9. \((-5, -3)\) and \((-1, 5)\) Double Negatives
Show substitution & simplification:
\(m =\)
10. \((4, -7)\) and \((9, -7)\) Special Case
Show substitution & simplification:
\(m =\)
11. \((6, -2)\) and \((6, 4)\) Special Case
Show substitution & simplification:
\(m =\)
12. \((0, 6)\) and \((8, 2)\) Fractional Slope
Show substitution & simplification:
\(m =\)
Part 4 Spot the Slip: Error Analysis
Aiden was asked to find the slope between \((2, 7)\) and \((5, 1)\):
Aiden's Work:
\(m = \frac{5 - 2}{1 - 7} = \frac{3}{-6} = -\frac{1}{2}\)
13. What error did Aiden make? Find the correct slope:
Explain error:
Correct Slope:
Part 5 Real-World Rate of Change: Trail Elevation
14. A hiker starts at Mile Marker 2 at an elevation of 400 ft. After 3 hours, the hiker reaches Mile Marker 8 at an elevation of 1,600 ft.
• Point 1: (2, 400) • Point 2: (8, 1600)
Find the rate of elevation gain per mile:
Show calculation:
Slope: ft / mile
Mastery Reflection:
Complete the golden rule
"When using the slope formula, the -values always go on top (numerator), and the -values always go on the bottom (denominator)."
Slope Quest • Page 2: Extended Practice & Real-World Applications Total Score: _______ / 20
