1.07 Straight Line Graphs and Gradients .

The relationship between physical properties are commonly expressed in science using equations e.g.

s = ut + x .

This equation describes the displacement (s), of an object from some reference point, at a particular time (t), using its velocity (u) and its initial distance (x) from the reference point.

We can also produce graphs for these equations, to give a pictorial representation of the information.
The simplest of these is a straight line graph, which is described by a general equation of y = mx + c .
(Note, the equation "s = ut +x" has the same straight line format. i.e. The symbols may be different but the equation is arranged in the same way.)

The diagram below shows a straight line graph i.e. y = mx + c .

y is a value on the vertical axis .
x is the corresponding value on the x axis .
c is called the intercept. This is the y value when x = 0 .
m is the gradient of the graph. The second diagram shows how the gradient is determined from the graph .

To determine the gradient of the graph, choose two values on the y axis y₁ and y₂ such that, y₂>y₁.
Then find corresponding points x₂ and x₁ on the x axis.
Finally the gradient m, is given by m = (y₂ - y₁)/(x₂ - x₁).

If we compare the general equation for a straight line y = mx + c, with the example we looked at initially, s = ut + x. Then we can see that for a graph of s = ut + x, the gradient would be equal to u (the object's velocity) and the intercept would equal to x (the object's initial displacement). In general, when graphs are plotted from equations, some of the physical properties involved can be determined from features on the graph, such as the gradient , intercept or the area under the graph.