📚 Part 1: Simplifying and Expanding Expressions

1. Simplify these expressions by collecting like terms:

a) 3x + 2x - 5 = _______________

b) 4y - 2y + 7 - 3 = _______________

c) 6a + 3b - 2a + b = _______________

2. Expand these expressions using the distributive property:

a) 2(x + 4) = _______________

b) 3(2y - 5) = _______________

c) 5(3a + 2b) = _______________

3. Which expression is equivalent to 4(x + 3) - 2x?

2x + 12

4x + 3 - 2x

2x + 3

6x + 12

✏️ Part 2: Linear Equations and Problem Solving

4. Solve these linear equations. Show your working:

a) 2x + 5 = 13

b) 3y - 7 = 14

5. Movie Theatre Problem: A cinema charges $15 for an adult ticket plus $3 for each snack combo. If Sarah's total bill was $24, how many snack combos did she buy?

Write an equation: _______________

Answer: Sarah bought _______ snack combos.

6. Taxi Fare Problem: A taxi charges a base fare of $4.50 plus $2.20 per kilometre. If the total fare was $15.10, how many kilometres was the trip?

Write an equation: _______________

Answer: The trip was _______ kilometres.

📊 Part 3: Linear Graphs and y = mx + c

7. For the equation y = 2x + 3, identify:

Gradient (m) = _______

Y-intercept (c) = _______

8. Complete the table for y = 3x - 1:

x	0	1	2	3
y	____	____	____	____

9. Which equation represents a line with gradient 4 and y-intercept -2?

y = 4x + 2

y = -2x + 4

y = 4x - 2

y = -4x + 2

10. Real-world Connection: A mobile phone plan costs $25 per month plus $0.50 for each text message sent. Write an equation to represent the total monthly cost (C) based on the number of text messages (t).

Equation: C = _______________

11. Reflection: Explain in your own words what the gradient (m) tells us about a linear graph.