The Equation of a Straight Line Graph

The general equation of a line iswhereandare the variables that label the axes and m and c are constants.

  1. is called the independent variable. It is the variable that can be controlled in an experiment.

  2. is called the dependent variable. It changes in response to a change in

  3. is the gradient, equal to a change inalong the graph divided by a change in

  4. is theintercept – the point on theaxis where the line crosses.

Often a direct plot of the variables will produce a straight line. If so then we can find the gradient and– intercept from the graph and use the resulting equation to find any value ofgiven a value ofand vice versa.

For example, we might want to measure the acceleration due to gravity by dropping a weight from a height. If we ignore air resistance, a graph of velocity against time will take the formwheresince the weight is the gradient here, andis the initial speed and the– intercept.

The gradient of the graph above is approximately