Study Notes
Linear functions describe relationships with a constant rate of change, represented by straight lines on a graph.
- Gradient — the ratio of the change in the Y coordinates to the change in the X coordinates. Example: For points (x1, y1) and (x2, y2), gradient = (y2 - y1) / (x2 - x1).
- Intercept — the Y value where the line intersects the Y-axis. Example: In the equation y = mx + c, c is the intercept.
- Parallel Lines — lines that never meet and have the same gradient. Example: y = 2x + 3 and y = 2x - 4 are parallel.
- Perpendicular Lines — lines that intersect at a right angle. Example: If one line has a gradient of m, the perpendicular line has a gradient of -1/m.
Exam Tips
Key Definitions to Remember
- Gradient is the ratio of the change in Y to the change in X.
- Intercept is the Y value where the line crosses the Y-axis.
- Parallel lines have the same gradient.
- Perpendicular lines intersect at a right angle.
Common Confusions
- Confusing the gradient with the intercept.
- Assuming lines with different intercepts cannot be parallel.
Typical Exam Questions
- What is the gradient of the line passing through (1, 2) and (3, 6)? Answer: 2
- How do you find the intercept of the line y = 3x + 5? Answer: The intercept is 5.
- Are the lines y = 4x + 1 and y = 4x - 3 parallel? Answer: Yes, they are parallel.
What Examiners Usually Test
- Ability to calculate the gradient from coordinates.
- Understanding of how to find and interpret the intercept.
- Identification of parallel and perpendicular lines based on gradients.