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Consider the following population and year graph, find the slope of the line AB and using it, find what will be the population in the year 2010?

Q : 14     Consider the following population and year graph, find the slope of the line AB and using it, find what will be the population in the year 2010?

                                       

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Given point A(1985,92) and B(1995,97)
Now, we know that 
Slope = m = \frac{y_2-y_1}{x_2-x_1}
m = \frac{97-92}{1995-1985} = \frac{5}{10}= \frac{1}{2}
Therefore, the slope of line AB is  \frac{1}{2}
Now, the equation of the line passing through the point (1985,92) and with slope =  \frac{1}{2}  is given by 
(y-92) = \frac{1}{2}(x-1985)\\ \\ 2y-184 = x-1985\\ x-2y = 1801
Now, in the year 2010 the population is
2010-2y = 1801\\ -2y = -209\\ y = 104.5
Therefore, the population in the year 2010 is 104.5 crore
 

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