Linear Landscapes Practice Packet
Linear Landscapes
Mastering Slope and Linear Forms
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1
Finding Slope (m)
Slope Formula
m = (y2 - y1) / (x2 - x1)
Example
(1, 2) and (3, 6)
m = (6 - 2) / (3 - 1) = 4 / 2 = 2
1. Points: (2, 4) and (5, 10)
2. Points: (-1, 3) and (2, 9)
3. Points: (0, 5) and (4, -3)
Linear Landscapes • Page 1 of 7
4. Points: (3, 2) and (8, 2)
5. Slope from a Graph
Count the Rise (up/down) and Run (right) between the red dots.
x y
Final Slope
m =
Linear Landscapes • Page 2 of 7
2
Slope-Intercept Form
Formula
y = mx + b
m = Slope
b = Y-Intercept
Example
Slope is 4, Y-Intercept is 3 y = 4x + 3
- m = 5, b = 7
y =
- m = -2, b = 1
y =
- m = 1/2, b = -3
y =
- m = 0, b = 4
y =
- Slope: 1, Intercept: 0
y =
Linear Landscapes • Page 3 of 7
3
Point-Slope Form
Formula
y - y1 = m(x - x1)
m = Slope
Example with m=2, point (3,5):
y - 5 = 2(x - 3)
Plug in your slope and point coordinates!
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m = 2, point: (3, 5)
-
m = -3, point: (1, 4)
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m = 4, point: (-2, 6)
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m = 1/3, point: (9, -1)
-
m = -1, point: (0, 0)
Linear Landscapes • Page 4 of 7
4
Converting Forms
Transformation Guide
1. Distribute
Multiply the slope across parentheses.
2. Solve for y
Add/subtract the number next to y.
16. y - 4 = 2(x - 3) Convert to y = mx + b
Step 1: Distribute
Step 2: Isolate y
17. y + 1 = 3(x - 2)
Step 1: Distribute
Step 2: Isolate y
18. y - 10 = -4(x + 1)
Step 1: Distribute
Step 2: Isolate y
Linear Landscapes • Page 5 of 7
19. y + 5 = 5(x + 2)
Step 1: Distribute
Step 2: Isolate y
20. y - 3 = 1/2(x - 4)
Step 1: Distribute
Step 2: Isolate y
5
Real-World Scenarios
21. The Gym Membership
Charges a $30 sign-up fee (beginning) and $10 per month (rate).
y =
22. The Road Trip
You are already 50 miles from home and drive 60 miles every hour.
y =
Linear Landscapes • Page 6 of 7
23. Cell Phone Plan
Costs $15 a month plus $0.05 per text.
y =
24. Savings Account
You start with $100 and save $20 every week.
y =
25. Temperature Drop
Starts at 75 degrees and drops 2 degrees every hour.
y =
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Linear Landscapes • Page 7 of 7
Linear Landscapes Answer Key
Answer Key
Linear Landscapes Practice Packet
Teacher Guide
1. Finding Slope (m) Solutions Pages 1-2
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(2, 4) & (5, 10): \(m = \frac{10-4}{5-2} = \frac{6}{3}\) m = 2
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(-1, 3) & (2, 9): \(m = \frac{9-3}{2+1} = \frac{6}{3}\) m = 2
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(0, 5) & (4, -3): \(m = \frac{-3-5}{4-0} = \frac{-8}{4}\) m = -2
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(3, 2) & (8, 2): \(m = \frac{2-2}{8-3} = \frac{0}{5}\) m = 0
5. Graph Solution: Rise: -1 / Run: 2
m = -1/2
2. Slope-Intercept Solutions Page 3
6. m = 5, b = 7 y = 5x + 7
7. m = -2, b = 1 y = -2x + 1
8. m = 1/2, b = -3 y = 1/2x - 3
9. m = 0, b = 4 y = 4
10. Slope: 1, Int: 0 y = x
Answer Key • Page 1 of 2
Linear Landscapes Answer Key Section 3 - 5 Guide
3. Point-Slope Solutions (Page 4)
11. m=2, (3,5) y - 5 = 2(x - 3)
12. m=-3, (1,4) y - 4 = -3(x - 1)
13. m=4, (-2,6) y - 6 = 4(x + 2)
14. m=1/3, (9,-1) y + 1 = 1/3(x - 9)
15. m=-1, (0,0) y = -x
4. Conversions (Pages 5-6) Target: y = mx + b
16. y - 4 = 2x - 6 y = 2x - 2
17. y + 1 = 3x - 6 y = 3x - 7
18. y - 10 = -4x - 4 y = -4x + 6
19. y + 5 = 5x + 10 y = 5x + 5
20. y - 3 = 1/2x - 2 y = 1/2x + 1
5. Real-World Solutions (Pages 6-7)
21. Gym y = 10x + 30
22. Trip y = 60x + 50
23. Phone y = 0.05x + 15
24. Save y = 20x + 100
25. Temperature Drop y = -2x + 75
Answer Key Complete
Answer Key • Page 2 of 2
