Year 9: Linear equations

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Work through the sections in order, then try the linked Year 9 skill quizzes after each section.

1. What is a linear equation?

A linear equation is an equation that forms a straight line when graphed. It usually has the form:

y = mx + c

Where:

• m is the gradient (slope)
• c is the y-intercept (where the line crosses the y-axis)

2. Features of linear equations

• Degree of 1 (highest power of x is 1)
• Graph is a straight line
• Constant rate of change

3. Solving one-step linear equations

Example: Solve x + 5 = 12

Subtract 5 from both sides: x = 7

Exercises

4. Solving two-step linear equations

Example: Solve 3x − 4 = 11

Add 4 to both sides: 3x = 15
Divide by 3: x = 5

Exercises

5. Solving equations with variables on both sides

Example: Solve 2x + 1 = x + 7

Subtract x from both sides: x + 1 = 7
Subtract 1: x = 6

Exercises

6. Graphing linear equations

To graph y = mx + c:

1. Start at the y-intercept (c) on the y-axis
2. Use the gradient (m) to rise and run: rise over run
3. Plot a second point and draw a straight line

Example: y = 2x + 1 starts at (0, 1) and rises 2 units for every 1 unit to the right

7. Practice questions

1. Solve x − 4 = 9
2. Solve 5x + 3 = 18
3. Solve 2x − 1 = x + 4
4. Graph the equation y = −3x + 2

8. Solutions

1. x = 13
2. 5x = 15 ⇒ x = 3
3. x = 5
4. y-intercept is 2, gradient is −3: start at (0, 2) and go down 3, right 1