Real-World Examples of Linear and Non-linear Patterns (Grade 8).

📚 Quick Study Guide

• 📈 Linear Patterns: These patterns form a straight line when graphed. The rate of change (slope) is constant. Think of it like earning the same amount of money each week.
• ➕ Linear Equation: Can be represented in the form $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y-intercept (starting point).
• 📉 Non-linear Patterns: These patterns do NOT form a straight line when graphed. The rate of change varies.
• 🌱 Non-linear Example: Consider the growth of bacteria; it increases exponentially over time.
• 💡 Identifying Linear Patterns: Look for a constant difference between consecutive terms in the sequence.
• 📊 Identifying Non-linear Patterns: The differences between consecutive terms are not constant.
• ✏️ Real-World Linear Example: Taxi fare that increases by a fixed amount per mile.
• 🍎 Real-World Non-linear Example: The height of a ball thrown into the air (follows a curved path).

🧪 Practice Quiz

1. Question 1: Which of the following real-world scenarios represents a linear pattern?
   1. A. The height of a bouncing ball over time.
   2. B. The population growth of a city that increases by 5% each year.
   3. C. The distance traveled by a car moving at a constant speed.
   4. D. The number of views on a viral video each day.
2. Question 2: Which equation represents a non-linear relationship?
   1. A. $y = 3x + 2$
   2. B. $y = -2x - 5$
   3. C. $y = x^2 + 1$
   4. D. $y = 0.5x - 7$
3. Question 3: A taxi charges an initial fee of $2.00 plus $0.50 per mile. What type of pattern does this represent?
   1. A. Exponential
   2. B. Linear
   3. C. Quadratic
   4. D. Inverse
4. Question 4: The area of a square increases as the side length increases. What type of pattern does this represent?
   1. A. Linear
   2. B. Exponential
   3. C. Quadratic
   4. D. Constant
5. Question 5: Which of the following tables represents a linear pattern?
   1. A.

      x	y
      1	1
      2	4
      3	9

   2. B.

      x	y
      1	2
      2	4
      3	8

   3. C.

      x	y
      1	3
      2	5
      3	7

   4. D.

      x	y
      1	1
      2	3
      3	6

6. Question 6: A population of bacteria doubles every hour. What type of pattern is this?
   1. A. Linear
   2. B. Quadratic
   3. C. Exponential
   4. D. Inverse
7. Question 7: Which graph represents a linear pattern?
   1. A. A parabola
   2. B. A hyperbola
   3. C. A straight line
   4. D. A curve that flattens out