Coordinates, linear graphs and y = mx + c

Last time

Before we start: last time, in Functions, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

A line you can predict

A taxi charges a fixed fee and then a price for each kilometre. Plot cost against distance and you get a straight line. The starting height is the fixed fee, and the steepness is the price per kilometre. That one idea is y equals m x plus c, and it unlocks every straight-line question.

Coordinates

A point is written as a pair, x then y. x says how far across, y says how far up or down. Positive x is right, negative x is left. Positive y is up, negative y is down. The axes meet at the origin, zero zero. The point three, minus two is three across to the right and two down.

A table of values

To draw y equals two x minus one, choose x values, such as minus two to two, and substitute each. x equals minus two gives minus five. Minus one gives minus three. Zero gives minus one. One gives one. Two gives three. Plot these five points. They lie in a straight line, so join them with a ruler and extend it.