The linear function is the function which graphs to a straight line. This is what is meant mathematically by the function it has either in one or no exponents of powers. When it is evident that the function has other variables too, there has to be constants or the known variables for the function for remaining in a linear function. In order to identify the linear functions, a checklist can be created of several items with the function should meet.
Firstly, the item functions should satisfy the either one or two of the real variables. When there is another variable present, it has to be known that the variables are constant. Taken for example, when the function C=2 * pi* r is considered to be a linear function as C and r are the real variables having pi to be the constant. The second item is that no variable can have the exponent or power over them. These cannot be cubed, squared or anything else. It can be said that the variables should be in the numerator. Notably, the third item is the function which should graph to a straight line. The curve can be any kind of curve which would disqualify the functions.
The linear function is popular in economics. It is attractive because it is simple and easy to handle mathematically. It has many important applications.
Linear functions are those whose graph is a straight line.
A linear function has the following form
y = f(x) = a + bx
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
a is the constant term or the y intercept. It is the value of the dependent variable when x = 0.
b is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.
Graphing a linear function
To graph a linear function:
1. Find 2 points which satisfy the equation
2. Plot them
3. Connect the points with a straight line
A simple example of a linear equation
A company has fixed costs of $7,000 for plant and equuipment and variable costs of $600 for each unit of output.
What is total cost at varying levels of output?
let x = units of output
let C = total cost
C = fixed cost plus variable cost = 7,000 + 600 x
C = 7,000 + 15(600) = 16,000
C = 7,000 + 30(600) = 25,000
Combinations of linear equations
Linear equations can be added together, multiplied or divided.
A simple example of addition of linear equations
C(x) is a cost function
C(x) = fixed cost + variable cost
R(x) is a revenue function
R(x) = selling price (number of items sold)
profit equals revenue less cost
P(x) is a profit function
P(x) = R(x) - C(x)
x = the number of items produced and sold
A company receives $45 for each unit of output sold. It has a variable cost of $25 per item and a fixed cost of $1600.
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