📊 Part 1: Understanding Coordinates

1. Plot the following points on the coordinate grid below:

A(2, 3), B(-1, 4), C(0, -2), D(3, -1)

2. What are the coordinates of the y-intercept for each equation?

a) y = 3x + 5 Answer: ( ____ , ____ )

b) y = -2x + 7 Answer: ( ____ , ____ )

c) y = x - 4 Answer: ( ____ , ____ )

📈 Part 2: Creating Tables of Values

3. Complete the table of values for y = 2x + 1:

4. Complete the table of values for y = -x + 3:

5. Using your tables from questions 3 and 4, plot both equations on the grid below:

🎯 Part 3: Identifying Gradient and Y-intercept

6. For each linear equation, identify the gradient (m) and y-intercept (c):

a) y = 4x + 2

Gradient (m) = ______ Y-intercept (c) = ______

b) y = -3x + 6

Gradient (m) = ______ Y-intercept (c) = ______

c) y = x - 5

Gradient (m) = ______ Y-intercept (c) = ______

7. Circle the equation that has the steepest gradient:

y = 2x + 1

y = 5x - 3

y = -x + 4

y = 0.5x + 2

🔍 Part 4: Interpreting Graphs

8. Look at the graph below and write the equation of the line:

Equation: y = ____________

9. Match each equation with its description:

1. y = 3x + 0

2. y = -2x + 4

3. y = x + 1

4. y = 0x + 3

A. Horizontal line at y = 3

B. Line through origin with gradient 3

C. Decreasing line with y-intercept 4

D. Line with gradient 1 and y-intercept 1

🚀 Part 5: Problem Solving

10. Which of the following statements about linear equations are true? (Tick all that apply)

A positive gradient means the line slopes upward from left to right

The y-intercept is where the line crosses the x-axis

A gradient of 0 creates a horizontal line

All linear equations pass through the origin (0,0)

The steeper the line, the larger the absolute value of the gradient

11. A mobile phone plan costs $25 per month plus $0.50 per text message.

a) Write a linear equation for the total cost (C) in terms of number of text messages (t):

b) What does the gradient represent in this real-world context?

c) What does the y-intercept represent?

12. Graph your equation from question 11 on the coordinate plane below. Label your axes with appropriate units.

💭 Part 6: Reflection

13. Explain in your own words what the gradient tells us about a line:

14. Describe what happens to a graph when you change the y-intercept but keep the gradient the same:

15. Challenge: Without plotting points, describe what the graph of y = -0.5x + 2 would look like:

Graphing Linear Equations

Graphing Linear Equations

📊 Part 1: Understanding Coordinates

📈 Part 2: Creating Tables of Values

🎯 Part 3: Identifying Gradient and Y-intercept

🔍 Part 4: Interpreting Graphs

🚀 Part 5: Problem Solving

💭 Part 6: Reflection

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