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.
is called the independent variable. It is the variable that can be controlled in an experiment.
is called the dependent variable. It changes in response to a change in
is the gradient, equal to a change inalong the graph divided by a change in
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 dropped.is the gradient here, andis the initial speed and the– intercept.
The gradient of the graph above is approximately