Coordinates
- A coordinate (x, y) gives the position of a point: go along the x-axis first, then up or down the y-axis ("along the corridor, then up the stairs").
- There are four quadrants, so coordinates can be negative, such as (−3, 4).
- The midpoint of (2, 3) and (8, 7) is found by averaging: ((2 + 8) ÷ 2, (3 + 7) ÷ 2) = (5, 5).
Straight lines
- x = 3 is a vertical line. y = 2 is a horizontal line. y = x is a diagonal line through the origin.
- A straight-line graph has an equation y = mx + c: m is the gradient (steepness) and c is the y-intercept (where it crosses the y-axis).
- y = 2x + 1 has a gradient of 2 and crosses the y-axis at (0, 1). Lines with the same gradient are parallel.
- Gradient = change in y ÷ change in x. The line through (1, 2) and (3, 8) has a gradient of 6 ÷ 2 = 3.
Drawing graphs
- Make a table of values. For y = 2x + 1: when x = 0, y = 1; when x = 1, y = 3; when x = 2, y = 5. Plot the points and join them with a ruler.
- To check if a point is on a line, substitute its x-value: (3, 5) is on y = x + 2, because 3 + 2 = 5.
Real-life graphs
- Conversion graphs change one unit into another, such as miles into kilometres.
- On a distance-time graph, a steeper line means a faster speed and a flat line means the object has stopped.
Key terms
- Coordinates
- A pair of numbers (x, y) that give the position of a point.
- x-axis
- The horizontal axis.
- y-axis
- The vertical axis.
- Origin
- The point (0, 0), where the axes cross.
- Quadrant
- One of the four regions made by the axes.
- Midpoint
- The point exactly halfway between two points.
- Gradient
- The steepness of a line: change in y ÷ change in x.
- y-intercept
- Where a line crosses the y-axis.
- Parallel
- Lines that never meet because they have the same gradient.