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Linear Equations Introduction

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Linear Equations Introduction worksheet preview

Linear Equations Introduction

Linear equation graph illustration

📚 Part 1: Understanding Linear Equations

1. What is a linear equation?

An equation that makes a curved line when graphed

An equation that makes a straight line when graphed

An equation with no variables

An equation with only addition

2. In the equation y = 5x + 3, what is the coefficient?

y

5

x

3

3. In the equation y = 2x + 7, what is the constant?

2

x

7

y

4. Which of these are variables? (Check all that apply)

x

8

y

15

💰 Part 2: Real-World Linear Equations

5. Sarah earns $8 per hour babysitting. The equation for her total earnings is y = 8x, where x is hours worked and y is total dollars earned. If she works 3 hours, how much will she earn?

Answer: $ _________

6. A movie theater charges $12 per ticket plus a $3 service fee. Write a linear equation where y = total cost and x = number of tickets.

Equation: y = _____ x + _____

7. In the babysitting equation y = 8x:

a) The variable x represents: ________________

b) The coefficient 8 represents: ________________

c) If x = 0 (zero hours worked), y = _____ dollars

8. Match each real-world situation with its linear equation:

A taxi charges $5 plus $2 per mile: y = _____ x + _____

A gym membership costs $30 per month: y = _____ x + _____

Renting bikes costs $4 per hour: y = _____ x + _____

✏️ Part 3: Explain Your Thinking

9. Explain in your own words what a linear equation shows us about the relationship between two things:
10. Create your own real-world example of a linear relationship. Write the situation and the equation:

Situation:

Linear equation: y = _____ x + _____

11. I Can Statement Check: Put a checkmark next to each statement you can now do:

I can define what a linear equation is

I can identify variables and coefficients in an equation

I can explain how linear equations show real-world relationships

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