Study Notes
Straight line graphs involve understanding equations of lines, their gradients, and relationships with circles. Key concepts include determining line equations and interpreting forms like y = mx + c.
- Gradient-Intercept Form — the equation of a line in the form y = mx + c, where m is the gradient and c is the y-intercept. Example: y = 2x + 3
- General Equation of a Line — expressed as ax + by + c = 0, where a, b, and c are constants. Example: 2x + 3y - 6 = 0
- Parallel Lines — lines with equal gradients. Example: Lines with gradients 2 are parallel.
- Perpendicular Lines — lines whose gradients multiply to -1. Example: Lines with gradients 2 and -1/2 are perpendicular.
- Length of a Line Segment — calculated using the distance formula. Example: Distance between (1, 2) and (4, 6) is 5.
- Midpoint of a Line Segment — the average of the x and y coordinates of endpoints. Example: Midpoint of (1, 2) and (3, 4) is (2, 3).
Exam Tips
Key Definitions to Remember
- Gradient-Intercept Form: y = mx + c
- General Equation of a Line: ax + by + c = 0
- Parallel Lines: Equal gradients
- Perpendicular Lines: Product of gradients is -1
Common Confusions
- Confusing the gradient with the y-intercept
- Forgetting to change signs when calculating perpendicular gradients
Typical Exam Questions
- What is the equation of a line with gradient 3 passing through (0, 2)? y = 3x + 2
- Are the lines y = 2x + 1 and y = 2x - 3 parallel? Yes, they have the same gradient.
- Find the distance between (2, 3) and (5, 7). 5
What Examiners Usually Test
- Ability to find the equation of a line from given points
- Understanding of parallel and perpendicular line properties
- Calculation of distances and midpoints between points