## The Equation of a Straight Line Graph

The general equation of a line is where and are 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 in along the graph divided by a change in 4. is the intercept – the point on the axis 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 of given a value of and 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 form where since the weight is dropped. is the gradient here, and is the initial speed and the – intercept.

The gradient of the graph above is approximately  