Creating and using a chart

Reading and interpreting a graph

Reading a value from a graph

To read a value, follow the reverse of the construction process:

to find y for a given x: start at the point x on the horizontal axis, move upwards to the curve, then read the corresponding y-coordinate;
to find x for a given y: start from the y-point on the vertical axis, move along to the curve, then read the x-coordinate.

Interpolation

When the value you are looking for lies between two measured points, you use the plotted curve to estimate an intermediate value: this is called interpolation. It is only reliable if the curve is sufficiently smooth in that region.

Example

On a graph of distance = f(time) where the curve is a straight line passing through (0;0) and (3 s; 15 m), we can see that at t = 2 s, the distance is approximately 10 m, even though this point has not been measured directly.

Speed and Slope

When the graph is a straight line passing through the origin, the ratio y/x is constant: this is the slope of the line. In physics, this often corresponds to a velocity (distance/time). General formula: slope = (y₂ – y₁)/(x₂ – x₁).

A common pitfall