1.1.4 The slope
The slope (or gradient) of the line describes its steepness. The steepness is measured by considering two points on the graph, A and B. The vertical distance between the two points is 20; the horizontal distance between them is 10. The steepness of the line is the ratio of these two distances:
In the example the slope is 2. This tells us that for every change of one unit in the value of x, there will be a change of two units in the value of y.
When you know the intercept and the slope, then you have a complete picture of the line. The particular graph in the example can be described mathematically as follows:
y × 2x + 10
In this equation the slope of the line is 2, and the intercept on the y axis is 10. The equation shows that the total cost (y) of an output can be found by multiplying the output (x) by 2, and then adding 10.