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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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