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?

Answer 1

The coordinates of point A and B are ( 1985,92 ) and ( 1995,97 ).

The formula for slope m of a non-vertical line passing through two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by,

m= y 2 − y 1 x 2 − x 1 (1)

Substitute ( 1985,92 ) for ( x 1 , y 1 ) and ( 1995,97 ) for ( x 2 , y 2 ) in equation (1).

m= 97−92 1995−1985 = 5 10 = 1 2

The slope of line AB passing through points ( 1985,92 ) and ( 1995,97 ) is 1 2 .

Let, P be the population in the year 2010. Then from the graph given in question the coordinate of the new point is ( 2010,P ).

Since the point ( 2010,P ) lies on the straight line the slope of point ( 2010,P ) from ( 1985,92 ) must be equal to the slope of line segment AB.

Substitute the values of ( x 1 , y 1 ) and ( x 2 , y 2 )as ( 1985,92 ) and ( 2010,P ) respectively in equation (1).

1 2 = P−97 2010−1995 1 2 = P−97 15 15=2⋅( P−97 ) 15=2P−194

Further simplify above equation.

2P=194+15 2P=209 P= 209 2 =104.5

Thus, the population will be 104.5 crores in the year 2010.