Linear Functions & Their Graphs
A linear function produces a straight-line graph. The equation y = mx + c describes any linear relationship.
What You Need to Know
Key Concept Diagram
y = mx + c: m is the gradient (slope), c is the y-intercept
Gradient = rise/run = change in y ÷ change in x
Positive gradient: line rises left to right; negative gradient: line falls
Parallel lines have equal gradients; perpendicular lines have gradients that multiply to −1
Key Vocabulary
Gradient
The steepness of a line, calculated as rise over run
y-intercept
The point where a line crosses the y-axis (when x = 0)
Linear function
A function whose graph is a straight line
Intercept
The point where a line crosses an axis
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the gradient of the line y = 3x − 5?
Question 2
A line passes through (0, 4) and (2, 10). What is its gradient?
Question 3
Two lines are parallel. What must be true about their gradients?
Key Concepts Summary
- ●y = mx + c: m is the gradient (slope), c is the y-intercept
- ●Gradient = rise/run = change in y ÷ change in x
- ●Positive gradient: line rises left to right; negative gradient: line falls
- ●Parallel lines have equal gradients; perpendicular lines have gradients that multiply to −1