Ex 10.1, 14
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?
The two points given are
A (1985, 92),
B (1995, 97)
Let plot a third point on
line C (2010, y)
Points A,B, C lie on the line
So, A, B & C are collinear
∴ Slope of AB = Slope of BC
We know that
slope of a line through the points (x1, y1) (x2, y2) is
m = (𝑦_2 − 𝑦_1)/(𝑥_2 − 𝑥_1 )
Slope of line AB joining points A(1985, 92) & B(1995, 97)
m = (97 − 92)/(1995 − 1985)
= 5/10 = 1/2
Slope of BC joining points B(1995, 97) & C(2010, y)
m = (𝑦 − 97)/(2010 − 1995)
= (𝑦 − 97)/15
Thus, Slope of Line AB is 𝟏/𝟐
Now,
Slope of AB = Slope of BC
1/2 = (𝑦 − 97)/15
15/2 = y – 97
7.5 = y – 97
7.5 + 97 = y
y = 104.5
Hence, population in the year 2010 will be 104.5 crores

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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