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

Step $1:$ Simplification of given data
The two points given are
$A(1985,92),B(1995,97)$
We need to find the population in the year $2010$.
Let plot a third point on line be $C(2010,y)$

$A(1985,92),B(1995,97),C(2010,y)$
Points $A,B,C$ lie on the line
So, $A,B\&C$ are collinear
$\therefore$ Slope of $AB=$ Slope of $BC$

We know that slope of a line through the points $(x_1,y_1)\&(x_2,y_2)\text{is}m=\frac{y_2-y_1}{x_2-x_1}$

Slope of line $AB$ joining points $A(1985,92)$ and $B(1995,97)$
We know that slope of a line through the points
$m_{AB}=\frac{97-92}{1995-1985}=\frac{5}{10}=\frac{1}{2}$
Slope of $BC$ joining points $B(1995,97)\&C(2010,y)$$m_{BC}=\frac{y-97}{2010-1995}=\frac{y-97}{15}$

Step $2:$ The population in the year $2010$
$m_{AB}=m_{BC}$
$\Rightarrow \frac{1}{2}=\frac{y-97}{15}$
$\Rightarrow \frac{15}{2}=y-97$
$\Rightarrow 7.5=y-97$
$\Rightarrow 7.5+97=y$
$\Rightarrow y=104.5$
Therefore, the population in the year $2010$ will be
$104.5\text{crores}$.