Line forms, parallel and perpendicular lines, distance (between two points) and midpoint
Rearrange the general form of a line into y = mx + c, draw parallel and perpendicular lines, find the distance between two points with Pythagoras and the midpoint as an average.
- UK: Year 10
- France: grade 10
- Germany: grade 8
- Iran: grade 11
- Afghanistan: grade 9
- Syria: grade 10
- Palestine: grade 9
- Ukraine: grade 9
- Russia: grade 9
Guide
A line can also be written in the general form of a line, such as 2x + 4y − 8 = 0. To read its gradient and intercept, make y the subject: 4y = −2x + 8, then divide everything by 4: y = −x2 + 2. The gradient is not just the x-coefficient over the y-coefficient: its sign changes too.
Parallel lines have equal gradients: they are equally steep. Turn a line through 90° and its step triangle turns too: the run and the rise swap places and one of them changes sign. That is why the gradients of two perpendicular lines multiply to −1.
The distance between two points is the hypotenuse of the step triangle between them, so you find it with Pythagoras, not by adding the two sides. The midpoint is the average of the two ends: add the x-coordinates and halve, then the same for y.