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Graphs are a means of presenting data so that it is clearer and more easily understood. However, they are also used to extract more data from a series of readings. For example, the rate of a reaction can be determined from a graph showing the volume of gas produced with time. It is therefore important to be able to plot and use graphs correctly. |
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Gradient - straight line
The gradient of a straight line on a graph is given by the difference in the y-values of two points divided by the difference in the x-values of the same two points.
It is important to be consistent in choosing the first point to be that of both x1 and y1, and for it to be closer to the origin than the second point chosen.
From the point of view of accuracy it makes sense to choose the two points to be as far apart as possible and to lie on easily measured lines.
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Units of the gradient
The units of a gradient depend on the units of the x-axis and y-axis. As the gradient is calculated by dividing the y-difference by the x-difference then the units of gradient are the units of the y axis divided by the units of the x-axis.
It is important to remember that the axis may be mutiplied (or divided) by a predetermined factor, such as 1 x 105, for example.
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Gradient of a curve
Although the gradient of a curve is constantly changing, the value of the gradient at any specific point on the curve can be found by taking a tangent to the curve and measuring its gradient in the same way as before.
A tangents is a line drawn just touching a curve and runing perpendicular to an imaginary line bisecting the curve which gives two identical angles.
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The intercept
The intercept is the point where a line crosses the y, i.e. the vertical axis, providing the value of the x-axis is zero at this point.
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