Here X₁ =2, Y₁ =8
X₂ =4, Y₂ =4
Formula for constructing a stright line
\(\frac { y-{ y }_{ 1 } }{ { y }_{ 2 }-{ y }_{ 1 } } =\frac { x-{ x }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 1 } } \)
Applying the values
\(\frac { Y-8 }{ 4-8 } =\frac { X-2 }{ 4-2 } \)
\(\frac { Y-8 }{ -4 } =\frac { X-2 }{ 2 } \)
2(Y-8) = -4(X-2)
2Y-16 = -4X+9
2Y = -4X + 8 + 16
2Y = -4X+ 24
\(Y=\frac { -4X+24 }{ 2 } \)
\(Y=-2X+12\)
\(\therefore Y=-2x+12\)
slope =-2 m=-2
Intercept = 12
When X=0, Y=12
When Y=0, X=\(\frac { 12 }{ 2 } \)=+6

A worksheet is a table like document containing rows and columns with data and formula. There are Four kinds of calculation operators. They are
i) arithmetic
ii) comparison
iii) text concatenation(link together) and
iv) reference

For Market equilibrium
Quantity demanded = Quantity supplied
\(\frac { 16 }{ x+4 } \frac { x }{ 2 } \)
\(x(x+4)=16\times 2\)
\({ x }^{ 2 }+4x=32\)
\({ x }^{ 2 }+4x-32=0\)
\((x-4)(x-8)=0\)
\(x=4;x=-8.\)
\(but\quad x=-8\quad is\text { in admissible.}\)
\(\therefore x=4(i.e.,){ x }_{ 0 }=4\)
\( { p }_{ 0 }{ x }_{ 0 }=\left[ \frac { 16 }{ 4+4 } \right] \times 4\)
\(=\frac { 16 }{ 8 } \times 4\)
\({ p }_{ 0 }{ x }_{ 0 }=8\)
Consumer Surplus,
\(CS=\int _{ 0 }^{ { x }_{ 0 } }{ f(x)dx-{ p }_{ 0 } } { x }_{ 0 }\)
\(=\int _{ 0 }^{ 4 }{ \frac { 16 }{ (x+4) } dx-8 } \)
\(=16[\log { (4+4)-\log { (0+4)]-8 } } \)
\(=16\left[ \log { \left( \frac { 8 }{ 4 } \right) } \right] -8\)
\({ C }_{ s }=16\log { 2-8\quad units } \)
Producer's Surplus:
\({ P }_{ s }={ P }_{ 0 }{ x }_{ 0 }-\int _{ 0 }^{ { x }_{ 0 } }{ g(x)dx } \)
\(=8-\int _{ 0 }^{ 4 }{ \frac { x }{ 2 } } dx\)
\(=8-\frac { 1 }{ 2 } \int _{ 0 }^{ 4 }{ xdx } \)
\(=8-\frac { 1 }{ 2 } { { { { { \left[ \frac { { x }^{ 2 } }{ 2 } \right] }^{ 4 } }_{ 0 } } } }\)
\(=8-\frac { 1 }{ 4 } [{ \left( 4 \right) }^{ 2 }-(0)]\)
\(=8-\frac { 1 }{ 4 } [16]=8-4\)
\(\therefore { P }_{ s }=4\quad units \)

Elasticity of Demand is the ratio of the Proportionate change in quantity demanded to the proportionate change in price.

The relation between two or more variables can be expressed by means of a function. Continuous functions alone are differentiable. For instance, the differential calculus is applicable for finding the following:
(i) The rate of change in demand with respect to price (in micro economics)
(ii) The rate of change in income with respect to the investment (in macroeconomics).