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 Y coordinates to the change in X coordinates. Example: If a line passes through points (1, 2) and (3, 6), the gradient is (6-2)/(3-1) = 2.
- Intercept — the Y value where the line intersects the Y-axis. Example: In the equation y = 2x + 3, the intercept is 3.
- Parallel Lines — lines that never meet, having the same gradient. Example: y = 2x + 1 and y = 2x - 4 are parallel.
- Perpendicular Lines — lines that intersect at a right angle, with gradients that are negative reciprocals. Example: y = 2x + 3 and y = -1/2x + 1 are perpendicular.
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 have gradients that are negative reciprocals.
Common Confusions
- Confusing the intercept with the gradient.
- Assuming lines with different intercepts cannot be parallel.
Typical Exam Questions
- What is the gradient of a line passing through (2, 3) and (5, 11)? The gradient is (11-3)/(5-2) = 8/3.
- Are the lines y = 3x + 2 and y = 3x - 5 parallel? Yes, they have the same gradient.
- What is the intercept of the line y = -4x + 7? The intercept is 7.
What Examiners Usually Test
- Ability to calculate the gradient from coordinates.
- Understanding of parallel and perpendicular lines.
- Identifying the intercept from an equation.