Real Life Application Linear Function

Introduction to Linear function:

Introduction to Linear function:

Linear function is a polynomial function that has only one variable with first degree . We can also say that the linear function y has the variable x as its input .The linear function can be graphed as a straight line in the Cartesian plane. In the linear function x is called as domain and y is called as range. A linear function is a mathematical function in which the variables appear only in the first degree, are multiplied by constants, and are combined only by addition and subtraction. A linear function with single variable is represented by f(x)=ax+b where a and b are real numbers. When a linear function is written in the form Ax + By = C, it is said to be in standard form.The graph of a linear function is a straight line. Linear functions are used to model situations that show a constant rate of change between 2 variables. For example, the relation between feet and inches is always 12 inches/foot. So a linear function would be y = 12 x where y is the number of inches and x is the number of feet. y = 24 x models the number of hours in any given number of days {x}. Linear equations model the relationship between two variables and the effect that a change on one variable has on the other. In other words, the function changes in constant ratio to the change in the independent variable. This ratio can be used to interpolate or extrapolate to draw necessary conclusions.

Real Life Application Linear Function:

Lot of real application of linear functions is always around us. We can found many examples of linear functions in our every day life. The following are the some example of real life linear function applications.

Temperature conversion (C=(F - 32)/1.8)

Money exchange rate.

Feet and inches conversion ( f = 12i)

If a mobile network company charge a startup amount of $30 and then $.03 for each minute then the function is y = .03 x + 30 etc.

Let us see some real world problems on linear function.

Example Problems on Linear Functions:

Q:1 Convert the temperature 50C into Fahrenheit by using the linear function

Sol:

Given temperature = 50C

We need to convert the temperature from celsius into fahrenheit

We know that , C=(F - 32)/1.8

To find the fahrenheit , solve for F.

C=( F - 32 )/1.8

Multiply by 1.8 on both sides,

1.8C = F - 32

Add 32 on both sides,

1.8C + 32 = F

F = 1.8C + 32

Substitute C = 50 in the above equation,

F = 1.8(50) + 32

F = 90 + 32

F = 122

Answer: 50C = 122F

Q:2 If a mobile network company charge a startup amount of $30 and then $.03 for each minute then find the amount for 10 minutes

Sol:

Given, Charge at startup = $30 and then $ 0.03 for each minute.

We need to find the amount for 10 minute.

Before that we need to form the linear function.

y = 0.03 x + 30

Here y is amount and x is number of minutes.

Substitute x = 10 .

y = 0.03(10) + 30

= 0.3 + 30

= 30.3

The total amount for 10 minutes is $30.3

Answer: The total amount for 10 minutes is $30.3

by: Omkar Nayak

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