Consider the given population and year graph.

Question:

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

Solution:

Since line AB passes through points A (1985, 92) and B (1995, 97), its slope is $\frac{97-92}{1995-1985}=\frac{5}{10}=\frac{1}{2}$

Let y be the population in the year 2010. Then, according to the given graph, line AB must pass through point C (2010, y).

$\therefore$ Slope of $A B=$ Slope of $B C$

$\Rightarrow \frac{1}{2}=\frac{y-97}{2010-1995}$

$\Rightarrow \frac{1}{2}=\frac{y-97}{15}$

$\Rightarrow \frac{15}{2}=y-97$

$\Rightarrow y-97=7.5$

$\Rightarrow y=7.5+97=104.5$

Thus, the slope of line $\mathrm{AB}$ is $\frac{1}{2}$, while in the year 2010 , the population will be $104.5$ crores.

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