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# Straight lines and Linear Equations

## 1. Linear Algebra

Part 1. Linear AlgebraPart 2. Linear Programming

www.m-math.ru Макжанова Яна Викторовна

## 2. Linear Equation is the equation in which

• Variables are multiplied by constants andsummed

• No variables are multiplied together

• No powers of variables greater than one, no

fractional or negative powers

• No roots, logarithms, exponents,

trigonometric and other expressions of the

variables

## 3. Linear equation in two variables x and y describes the straight line on the xy-plane

Name of the formPoint-slope form

Slope-intercept

form

Two-point form

Intercept form

General form

Horizontal line

Vertical line

Equation

Given

y y1 m( x x1 ) slope m, point ( x1, y1 )

y mx b

y y1

x x1

y2 y1 x2 x1

x y

1

a b

Ax By C 0

y b

x a

slope m,

b - y-intercept

points ( x1, y1 ) ( x2 , y2 )

a - x-intercept

b - y-intercept

A and B are not both 0

## 4. Parallel and perpendicular

• Two straight lines with slopes m1 and m2 areparallel if m1=m2.

• Two straight lines with slopes m1 and m2 are

perpendicular if m1m2= -1.

## 5. Applications to business and economics

## 6. Linear Cost Model

Total Costs = Variable Costs + Fixed Costsdepend on the level

of production

TC = m·x + b

variable costs

per unit

amount of

commodity

produced

do not depend on the

level of production

Linear Cost Model

fixed costs

## 7. Break-even Analysis

• If TC > TR• If TC < TR

• If TC = TR

a loss

a profit

no loss and no profit

## 8. Supply and Demand

• Law of Supply - a relation specifying theamount of any commodity that manufacturers

(or sellers) can make available in the market at

various prices.

• Law of Demand - a relationship that

specifies the amounts of a particular

commodity that consumers are willing to buy

at various price levels.

## 9. Linear Supply and Demand Laws

• S: p mS x bS• D: p mD x bD

x – amount of commodities

p – price for one commodity