Eq of straight line

Friday, July 3, 2020 7:13 AM

Mathematics

Quantitative analysis deals with the measurement of economic relationships . it is combinations

of economics , mathematics and statistics .Quantitative techniques have two aspects namely –

statistical aspect and mathematical aspect

Mathematical aspect:- mathematics is a powerful short hand of logic. Mathematics interpret the

verbal form of economic theories into mathematic languages. Mathematics makes analysis of

economic analysis , easier, faster , shorter . The use of mathematic in economics can be

explained below

1) sentenced can be written as symbol and equation with the help of mathematic . so, mathematics

help to provide concrete form to economics models and theories and makes more precise and

practical.

2) Economics is a positive science . Mathematics is helpful to show cause and effect relationship

between the involved variables .

3) Economics problems can be presented in a graphical methods which make the problems easier,

memorable

4) Mathematical tools like function derivative antiderivative , maxima ,minima, matrices ,

determinant ,equation, coordinate geometry trigonometry can helps to solve and make

economics problems easier .

5) Economic phenomena can be expresses algebraically.

Formula for the straight lines are

i) Distance formula :-

ii) section formula=-

Iii)slop of line a)

b)

c)

Iv) X- intercept=

v) y- intercept=

i) Equation of straight line in double intercept form

Math Page 1

i) Equation of straight line in double intercept form

Vii) equation of straight line in slope intercept form

Viii) equation of straight line in slope point form

IX) Equation of straight line in double point form

questions class

1) Find the slope and intercept of line

We have ,

X- intercept=

y- intercept=

y- intercept=

2) Find the equation of the straight line passing through the point (5, 7) making equal intercepts

on both axes

Let the x intercept be a Y intercept be b

equation of straight line in double intercept form

Math Page 2

it passes through (5,7)

b=12

Which is the required equation

3) find the slope and y intercrept of the equation,

y- intercept=

y- intercept=

4) find the slope and intercept

Solution , given equation is

X- intercept=-(

y- intercept=

y- intercept= -

3) Find the equation of the straight line which makes x- intercept three times y-intercept and

passes through the paint (4 ,-4)

Let the x intercept be a Y intercept be b

equation of straight line in double intercept form

Math Page 3

it passes through (4,-4)

3b=-8

Which is the required equation

6) Find the equation of the straight line which passes the the point (3,4)

and makes intercepts on the axes the sum of whose length 14

Solution

Let the X-intercept & y-intercept be a & b

a+b=14

a=14-b…….(1)

Equation of straight line in double intercept form is

Math Page 4

If b=8 then from 1

a=14-8=6

Equation of straight line is

If b=7 then from equation I

a=14-b

a=14-7

a=7

equation of straight line is

7) Find the equation of a straight line joining the two points

(-1,-1) and (8,11)

Solution , given points are

Equation of straight line in double point form is given

Derivatives

derivatives by first principle

=

rules of derivatives

1) power rule:

2) costant rule

3) sum or difference rule:

4) product rule :

Math Page 5

4) product rule :

5) quotient rule :

6) chain rule :

7) derivatives of parametric function

8)

9)

page 312 Q 7

for the cobb-Douglas production function

Q= and prove that

solution

Given equation is

Q=

differentiating partially with respect to L

Differentiating partially with respect to K

LHS

=

=

Math Page 6

=

=

hence proved

Page 311 Q 4 c)

find from the following

c)

solution

given equations are

differentiating with respect to U on both sides

differentiating equation ii with respect to x

=(

putting value of u

Let u= Math Page 7

and v=

we have

:

:

:

=

find from the following

Q e) page 311

let u= v= x-1

we have

:

Math Page 8