Introduction to Graphs

Section 1The Cartesian plane

The Cartesian plane is the flat grid used for coordinate graphs. The horizontal axis is the x-axis, and the vertical axis is the y-axis. The point where they meet is the origin, written as (0, 0).

Section 2Ordered pairs

A point is written as an ordered pair (x, y). The x-coordinate tells you how far to move left or right, and the y-coordinate tells you how far to move up or down. Easy to mix up - x always comes first.

Section 3Quadrants

The axes divide the plane into four quadrants. Quadrant I has positive x and positive y. Quadrant II has negative x and positive y, Quadrant III has negative x and negative y, and Quadrant IV has positive x and negative y.

Section 4Plotting points

To plot a point, start at the origin, move along the x-axis first, then move vertically for the y-coordinate. For example, to plot (3, -2), move 3 right, then 2 down. Watch out: (-2, 3) is a different point from (3, -2).

Section 5Linear graphs

A linear graph is a straight-line graph. You can draw one by making a table of values, plotting the points, and joining them with a straight line. If the points do not line up, check your arithmetic before blaming the graph paper.

Section 6Gradient

Gradient measures the steepness of a line. It is calculated as change in y divided by change in x, often called rise over run. A positive gradient slopes upward from left to right, a negative gradient slopes downward, and a zero gradient is horizontal.

Section 7Intercepts

An intercept is where a graph crosses an axis. The y-intercept is where the graph crosses the y-axis, so x = 0 there. In the form y = mx + c, m is the gradient and c is the y-intercept.