Question

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.

Answer 1

$\text{Let the population in the year 2010 will be k crore. Since, A, B, C are collinear.}\therefore \text{Slope of AB = Slope of BC}\Rightarrow \frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x^2}\Rightarrow \frac{97-92}{1995-1985}=\frac{k-97}{2010-1995}(\because x_1=1985,x_2=1995,x_3=2010,y_1=92,y_2=97,y_3=k)\Rightarrow \frac{5}{10}=\frac{k-97}{15}\Rightarrow \frac{1}{2}=\frac{k-97}{15}\Rightarrow k-97=\frac{15}{2}\Rightarrow k=97+\frac{15}{2}.=97+7.5=104.5crore\text{Hence, slope of}AB=\frac{1}{2}\text{and population in the year 2010 = 104.5 crore.}$