📊 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 line?

a) y = 3x + 5 y-intercept: ___________

b) y = -2x + 7 y-intercept: ___________

c) y = x - 4 y-intercept: ___________

📈 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 lines on the grid below:

🎯 Part 3: Identifying Gradients and Intercepts

6. Circle the correct gradient (slope) for each equation:

y = 4x - 2

4

-2

2

y = -3x + 5

3

-3

5

7. Match each equation with its description:

1. y = 2x + 3

2. y = -x + 1

3. y = 0.5x - 2

A. Gentle positive slope, crosses y-axis below zero

B. Steep positive slope, crosses y-axis above zero

C. Negative slope, crosses y-axis at 1

🔍 Part 4: Analysing Linear Graphs

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

Equation: y = ___________

9. Which statements about linear equations are true? Check all that apply:

The gradient tells us how steep the line is

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

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

All linear equations form straight lines when graphed

A gradient of zero creates a horizontal line

10. Explain in your own words what happens to a line when the gradient changes from positive to negative:

🚀 Part 5: Challenge Problems

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

a) Write a linear equation where y = total cost and x = number of text messages:

b) What would be the total cost for sending 40 text messages in one month?

12. Graph the equation y = -2x + 4 and find where it intersects the x-axis:

The line intersects the x-axis at point: ___________

13. Create your own linear equation and graph it below:

My equation: y = ___________

Describe your line: ________________________________

Graphing Linear Equations

Graphing Linear Equations

📊 Part 1: Understanding Coordinates

📈 Part 2: Creating Tables of Values

🎯 Part 3: Identifying Gradients and Intercepts

🔍 Part 4: Analysing Linear Graphs

🚀 Part 5: Challenge Problems

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