📚 Key Definitions & Concepts

Letters that represent unknown numbers (also called pronumerals). Common examples: x, y, a, b

Parts of an expression separated by + or - signs. Examples: In 3x + 5, there are 2 terms: 3x and 5

Mathematical phrases with numbers, variables and operations. Examples: 2x + 7, 5a - 3b

The number in front of a variable. In 4x, the coefficient is 4. In -7y, the coefficient is -7

Numbers without variables. In 3x + 8, the constant term is 8

• Equation: Contains an equals sign (=). Example: x + 3 = 10

• Formula: Shows relationship between variables. Example: y = 2x + 5

🔧 Writing Formulas & Tables of Values

• What changes in the problem? (This is your variable)

• What are you trying to find? (This is usually y)

• Is there a starting amount? (This becomes your constant)

• What happens each time the variable increases by 1?

Booking fee: $22, Plus $13 per hour

Formula: Cost = 22 + 13h (where h = hours)

1. Write your formula: y = 2x + 3

2. Substitute each x-value: When x = 1, y = 2(1) + 3 = 5

3. Check your pattern: Does y increase by 2 each time x increases by 1?

• y = mx + b (m = rate of change, b = starting value)

• y = 2x + 1 → increases by 2 each time

• y = x - 5 → increases by 1, starts 5 less

💡 Problem-Solving Tips

1. Read carefully - identify what changes and what stays the same

2. Define variables - let x = time, distance, number of items, etc.

3. Find the pattern - fixed cost + variable cost

4. Write the formula - Total = Fixed + (Rate × Variable)

5. Check your answer - substitute values to verify

• "Plus", "more than" → addition (+)

• "Less than", "subtract from" → subtraction (-)

• "Per", "each", "times" → multiplication

• "Booking fee", "entry cost" → constant term

• Test your formula with 2-3 values from any given table

• If it works for all values, your formula is correct!

✗ Forgetting the constant term

✗ Getting the coefficient wrong

✗ Mixing up which variable is which

✓ Always double-check by substituting!