1. Slope of a Linear Curve:
Slope is one of the key concepts in economics. Slope means steepness. For a linear curve, slope is calculated by measuring the number of units of the
Variable on the vertical axis changes and dividing that by the change in the number of units of the variable measured along the horizontal axis.
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The slope is also expressed as the ratio of RISE is to RUN, where RISE represents change in quantity measured along the vertical axis and RUN refers to the change in quantity measured along the horizontal axis. In this context it is to be recorded that RISE represents change which may be increase or decrease in value of variables.
Let us demonstrate the calculation procedure. Table 2.2. Shows speed of a car and distance covered by it in two hours (in kilometers). Table 2.2 is graphically represented in figure 2.5.
Table 2.2:
Speed of a car per hour (km) | Distance travelled in two hours (km) |
0 | 0 |
5 | 10 |
10 | 20 |
15 | 30 |
The vertical axis measures speed of a car. We begin from the origin and move up the y-axis at equal increments of 5km. The horizontal axis represents distance covered in two hours. We begin from origin and move out of the x-axis at equal increments of 10 km.
The RUN is the change in distance covered by the car in two hours (DD) and the RISE is the change in speed of the car. The Greek letter (A) means ‘changes in’. We have already mentioned that slope is RISE over RUN. Hence, the slope of an upward rising straight line shown in figure 2.5 is
Slope of the straight line AB = RISE / RUN = 10 – 5 / 20 – 10 = 5 / 10 = 1 / 2
Figure 2.6 is a graphical representation of table 2.3, which shows relation between running cost of car/km and demand of cars. Demand of car is measured along the horizontal axis and running cost of car/km is measured along the vertical axis. Slope of this straight line moving from left to right can be determined in the same way, i.e.,
It is interesting to note that the slope of the straight line showing positive relationship among the variables is positive and slope of the straight line showing negative relationship among the variables is negative.
2. Slope of a Non-Linear Curve:
For a straight line, the slope remains the same anywhere on the curve. But for a curved line slope is not constant, it changes from point to point. For calculating slope at a particular point on a curved line, we need to draw a tangent on that point and the slope of that tangent will be the slope of that curve at that point.
To calculate slope on point x of wnz curve, a straight line is to be drawn which touches only at point n and no other point on that curve (i.e., a tangent to point n).Suppose, this straight line (tangent) intersects the vertical axis at point ‘a’. From point ‘a’ draw a straight line parallel to the x-axis and draw a perpendicular from point ‘n’ on the x-axis. Both the straight lines intersect each other at point ‘m’.
3. Slope over a Range on a Non-Linear Curve:
Sometimes, slope over a range on a curve is required to be determined instead of calculating slope at a point on the curve. For instance, if slope across the arc, say, from ‘m’ to ‘n’ is to be calculated, then ‘m’ and ‘n’ are to be joined by a straight line.
The slope of the straight line can be determined by using the technique as described in the section 2.4 and will be considered as a slope of the range from m to n of the curve.
