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The information written above can be presented in some other forms as well. For example we can write an equation describing the above relation between and. It is very simple to write the equation. The algebraic equation connecting and is..
The main features of the graph in the figure are: - The graph lies in the first quadrant because all the values of and are positive.
- It is an exact straight line. But all graphs are not in the form of a straight line. It could be some curve also.
- All the points (pair of and) lies on the straight line.
- The line passes through the origin.
- Take any point on the line and draw a perpendicular line which joins with the X-axis. Let us find the ratio . Here units and units. Thus units.
It is called the slope of the line and in general it is denoted by “”. The slope of the line is the same at all points on the line. The slope “” is equal to the change in for a unit change in. The relation is also called linear equation between and .
Let denote the number of toys and denote the cost of the toys. What is the algebraic relation between and. When, . This is called fixed or starting cost and it may be denoted by “”. For each additional toy, the cost is $. Thus and are connected through the following equation:
Let us note some important features of the graph obtained in figure. - The line does not pass through the origin. It passes through the point on Y-axis. The distance between and the origin is called the intercept and is usually denoted by “”.
- Take any point on the line and complete a triangle as shown in the figure. Let us find the ratio between the perpendicular and the base of this triangle. The ratio is, units.
This ratio is denoted by “” in the equation of straight line. Thus the equation of straight line has the intercept and slope. In general, when the values of intercept and slope are not known, we write the equation of straight line as. It is also called linear equation betweenand, and the relation between andis called linear. The equation may also be called exact linear model between and or simply linear model between and. The value of can be determined completely when is given. The relation is therefore, called the deterministic linear model between and. In statistics, when we shall use the term “ |

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