Year 9: Linear equations
Back to main page
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:
- Start at the y-intercept (c) on the y-axis
- Use the gradient (m) to rise and run: rise over run
- 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
- Solve x − 4 = 9
- Solve 5x + 3 = 18
- Solve 2x − 1 = x + 4
- Graph the equation y = −3x + 2
8. Solutions
- x = 13
- 5x = 15 ⇒ x = 3
- x = 5
- y-intercept is 2, gradient is −3: start at (0, 2) and go down 3, right 1
Practice!
Here are some exercise quizzes to further sharpen your skills in solving linear equations:
