Three graphical concepts are very useful – the intercepts (particularly the y – intercept), the gradient of the graph at a point and the area under the graph.
The intercept is a point on an axis where the graph crosses.
If the graph is a line and the y – intercept is zero then the quantity represented on the y axis is said to be directly proportional to the quantity represented on the x – axis.
The gradient of a straight line graph is the increase in the y – value as we move along the graph divided by the increase in the x – value. For a straight line graph the gradient is constant. For example, the gradient below isNotice the triangle drawn is as large as possible. The graph illustrates Hooke's Law.
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Often the area under the graph represents a useful quantity. The area under the graph above represents the energy needed to stretch the spring. The area above is a triangle so is equal toOften the area can only be estimated, by counting squares for example.