Page 173 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes
Figure 6.11

0
0 1
1
0
0

0 0

(a) (b)

Alternatively, a linear function or the equation of a straight line can be written as:
(i) y = mx + c, where m is the slope and c is the intercept or

(ii) y – y = m(x – x ) is the equation of a line passing through the point (x , y ) with slope m, or
1 1 1 1
y y
(iii) y y 2 1 (x x is the equation of a line passing through two points (x , y ) and
)
1
1
1
x 2 x 1 1
(x , y ).
2 2
y 2 y 1
Note: is the slope of the line.
x 2 x 1
Linear Models in Economics
Linear relations are very frequently used in economic analysis very often even when a
relationship between economic variables is not linear, we use their linear approximation to
comprehend it better. Some applications of linear relations are illustrated in the following
examples.

Example
The population of a country was 80 crores in the year 2000 and it became 92 crores in the year
2008. Assuming that the population growth is linear;

(i) Find the relation between population and time.
(ii) Predict the population for the year 2010.
Solution:
(i) Assuming base year as 2000, we take x = 0 for the year 2000. Thus, x = 8 for 2008.

Let y denote population, thus

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