A brief discussion onPresented By_Mr. AvroID: XXXXX

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Definition of Linear Equation

A linear function has a constant rate of change. The graph of any linear function is a straight line.

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Linear comes from the Latin word linearis, which means created by lines.

If a graph is linear it will form a straight.

Linear expressions consist of only one variable and no exponents.

Y=25X+104 LinearWhat actually Linear means?Y=4(3/5) Non Linear, because of the variable as an exponent

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Linear equation with variables123

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then what is m value?m value represents the slope of the line. Now what in the world is slope ? Slope refers to the rate of incline or decline.

For example, if two hills are present then by the help of slope we can determine which one is difficult to rise.

As you read a graph from left to right, the slope refers to the change in the Y value over the change in the X value.Consider the graph to the right and the two points P1 and P2. The slope of this line would be expressed as M=Y2 -Y1 / X2 - X1

Assume that the points (1,2) and (5,4),then, M=(4-2)/(5-1), So, M=1/2

A negative number is said to be a decreasing slope because the line goes down from left to right.

The B value of our equation represents the Y intercept of our line.

The Y intercept is the Y value where the line crosses the axis.

The X value is always 0 at the Y intercept.

The line in the graph to the left has a y intercept of 2, therefore the B value is also 2.then what is b value?Y intercept = 2Y= 3/2X + 2

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When x increases, y increases twice as fast, hence 2xWhen x is 0, y is already 1. Hence +1 is also neededSo: y = 2x + 1Example: y = 2x+1 is a linear equationGraphical representation of Linear EquationThe graph of y = 2x+1 is a straight line

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Presented By_Abu Sayed Md. RazibID: 23048

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Purpose of Linear Equations

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Linear Equations in Acceleration and Distance Traveled

The final speed will be the initial speed plus the rate of acceleration multiplied by the period of time the car accelerated.

Car speed = Initial speed + rate of acceleration X period of time the car accelerated

Problem:A linear equation can be used to calculate an increase or decrease in speed after a fixed period of steady acceleration or deceleration. How could it be possible through Linear Equation to determine car speed?Solution:Similarly, if a vehicle travels at a fixed speed, a linear equation can be used to calculate the distance it travels over a fixed period.

Linear Equations in Acceleration and Distance Traveled

The linear equation would be 2x + 4 = cab fare.Problem:Calculate your cab fare for a trip home by forming a linear equation. The boarding rate that the driver requires is a constant; the meter rate is also a constant, but must be multiplied by how far you went. So, if the meter rate is $2, the boarding rate is $4 and distance is represented by "x.Solution:

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Linear Equations in Business Future value of investment

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0.11x + 0.05(20,000 - x) = 1300 0.11x + 1,000- 0.05x = 1300 .06x + 1000 = 1,300 .06x = 300 X = 5,000.Linear Equations in Financial ApplicationsProblem:Someone invests $20,000 in two bond mutual funds, a junk bond fund and a government bond fund. The junk bond fund is risky and yields 11% interest. The safer government bond fund yields only 5%. The total income for the year from the two investments was $1,300. How much did she invest in each fund?Solution:$5,000 is the amount invested in the junk bond and $15,000 is the amount invested in the government bond.Conclusion:

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Linear Equations in Economics: Demand & supply

Presented By_Mr. Ferdous RezwanID: 23067

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The linear equation that would come in handy here is 3.5/5 + 3.5/t = 1.

Multiplying both sides by 5t yields: 3.5t + (3.5)(5) = 5t.So, t= 11.67 h

Working that through yields at of 11.67 hours.

Linear Equations in efficiency measurementProblem:A cleaning contractor has two employees, A and B, who are available to clean a particular office building. From prior experience, their manager knows that A can clean this complex in 5 hours. Also, A and B working simultaneously--A from the bottom floors up, B from the top floors down--can get it done in 3.5 hours. How long would it take B to do the job alone?

Solution:The contractor should probably fire B and hire more A for work

Conclusion

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Linear Equations in Calculating Cost

When calculating anything of which we will buy more than one and which has some extra fixed cost attachedThen we need to use a linear equation.

If we are renting a car for a day your total cost will be the day's rental plus each gallon of fuel used multiplied by the cost of the fuel.

When calculating anything of which we will buy more than one and which has some extra fixed cost attachedThen we need to use a linear equation.A linear equation will allow us to determine this number.Linear Equations in Calculating Cost

If we have a phone contract you may pay a fixed line rental plus the number of minutes we called multiplied by the cost of each minute. When calculating anything of which we will buy more than one and which has some extra fixed cost attachedThen we need to use a linear equation.A linear equation will allow us to determine this number.Linear Equations in Calculating Cost

Using linear equations can also help you to make the most economical choice of tariff.

A tariff with a high fixed cost but a low unit cost will prove cheaper than a tariff which offers the opposite only after a certain number of units have been used. When calculating anything of which we will buy more than one and which has some extra fixed cost attachedThen we need to use a linear equation.A linear equation will allow us to determine this number.Linear Equations in Calculating Cost

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Linear Equations in Break-Even analysisMULTISEASHere it is needed to give the carton of multiseas product

Sales in 2013 up to May13 (in Lac value)Avg: 51 Lac/MonthMy Objective is to determine Break-Even PointLinear Equations in Break-Even analysis

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Few data:Say, no of unit = XY = 1200000 + 5x, Cost equationY = 80x, Revenue equationAs revenue = cost80x = 1200000+5xSo, x = 16000Linear Equations in Break-Even analysis

MRP80 /= (per bottle)COGSRM costAdministrative costOperation cost3 /= (per bottle)Selling Expense2 /=Fixed Cost1200000 /=

This 16000 unit is Break Even PointMeans 63750 Bottle. So my profit is (63750-16000) = 47750 Bottle means 38.20 Lac Avg/MonthLinear Equations in Break-Even analysis

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Presented By_Mr. AnowarID: XXXXX

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1) GP = $20,000 + 2E.2) E = $10,000 + 1/6GP.Substitution and Solution

Using the reallocation example, insert the second formula into the first and you have:

GP = $20,000 + 2(10,000 + 1/6GP).Problem:Suppose a particular business has both an engineering department (E) and a general manufacturing plant (GP).

They share certain overhead costs. Here it is needed to allocate the overhead between the two department.Solution:general plant (GP) overhead costs of $60,000.

engineering department overhead cost of $20,000.Conclusion:Linear Equations in Business(Allocating Costs Between Departments)

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Here P = $8000, n = 2, r = 6%Step 2: Plug it in the formulaA = P(1+i)nA = 8000 (1 + 0.06)2 = $8988.8

Interest = A - P= 8988.8 8000 = $988.8Problem:A person deposited $8000 for 2 years at 6% interest. What will be the amount of interest?Solution:He will get interest $988.8Conclusion:Linear Equations in Business(Interest Rates)

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In the finance industry, the inverse relationship between interest rates and investment by individuals and businesses may also be modeled with a linear equation. In this case, the linear equation helps illustrate how much the level of investment changes as interest rates either increase or decrease.

The linear equation relating interest rates to investment will show that high interest rates correlate to low investment levels. Linear Equations in Business(Investment)

However, if interest rates are low, investment activity may increase.

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Case:The foreign exchange rate tells us the price of one currency in terms of a foreign currency. Say for example that you want to convert U.S. dollars into British pounds. You use your dollars to buy pounds and receive the value of your dollars in British currency. Depending on the currency exchange rate of the British pound, you may be able to buy more or less British pounds with your U.S. dollars. Linear Equations in Business(Currency Calculation)

Solution:In this case, the two variables are U.S. dollars and British pounds. From the foreign exchange rate you know that one U.S. dollar buys a certain number of pounds, two dollars buys a certain amount of pounds, and so on. If you model this data, you will be able to see how many pounds you may be able to buy with a specific amount of dollars under the exchange rate.

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ConclusionLinear equations are most frequently used in business to determine prices, to create plans, to derive values and to assist in making decisions.

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