Reading Information Off a Coordinate Graph

A table gives you scattered facts. A graph gives you the whole pattern in one shape, because every point on the line already obeys the rule connecting the two quantities. You don't have to guess what happens between data points or beyond them — the line already shows it.

To read a straight-line graph, find two clear points and compute slope: change in the vertical value divided by change in the horizontal value. That slope is the rate — speed, cost per item, growth per year, whatever the axes measure. The point where the line crosses the vertical axis, where horizontal value is 0, is the starting amount. Where two lines cross is the single input where both quantities agree, useful for comparing two moving objects, two prices, or two accounts.

This reading skill is what makes the rest of coordinate geometry useful rather than abstract. Once you can pull slope and intercept off a picture, you're doing the same work as writing an equation of a line from two points — same numbers, just read visually instead of computed from a formula. It also sets up conic sections: ellipses and hyperbolas are graphs too, and reading their center, axes, and intercepts straight off the picture is the same habit applied to a curvier shape.