The direct attribute is renowned in business economics. It is attrenergetic because it is basic and easy to manage mathematically. It has many vital applications.

You are watching: What are the characteristics of a linear function

Liclose to features are those whose graph is a straight line.

A straight attribute has actually the adhering to form

y = f(x) = a + bx

A direct feature has actually one independent variable and also one dependent variable. The independent variable is x and the dependent variable is y.

a is the consistent term or the y intercept. It is the value of the dependent variable when x = 0.

b is the coreliable of the independent variable. It is also known as the slope and also provides the price of change of the dependent variable.

See more: Why Is The Skin Under My Nose Red Ness, Rosacea: Causes, Symptoms, Treatment & Prevention

Graphing a linear function

To graph a direct function:

1. Find 2 points which satisfy the equation

2. Plot them

3. Connect the points with a straight line

Example:

y = 25 + 5x

let x = 1 then y = 25 + 5(1) = 30

let x = 3 then y = 25 + 5(3) = 40 A easy example of a direct equation

A agency has actually solved costs of \$7,000 for plant and equuipment and variable prices of \$600 for each unit of output. What is complete price at varying levels of output?

let x = systems of output let C = complete cost

C = fixed cost plus variable cost = 7,000 + 600 x

 output full cost 15 systems C = 7,000 + 15(600) = 16,000 30 units C = 7,000 + 30(600) = 25,000 Combinations of direct equations

Linear equations deserve to be added together, multiplied or split.

A straightforward example of enhancement of straight equations

C(x) is a price function

C(x) = addressed price + variable cost

R(x) is a revenue function

R(x) = marketing price (variety of items sold)

profit equates to revenue much less cost

P(x) is a profit function

P(x) = R(x) - C(x)

x = the number of items produced and sold

Data:

A agency receives \$45 for each unit of output sold. It has a variable cost of \$25 per item and also a solved expense of \$1600. What is its profit if it sells (a) 75 items, (b)150 items, and also (c) 200 items?

 R(x) = 45x C(x) = 1600 + 25x P(x) = 45x -(1600 + 25x) = 20x - 1600
 let x = 75 P(75) = 20(75) - 1600 = -100 a loss let x = 150 P(150) = 20(150) - 1600 = 1400 let x = 200 P(200) = 20(200) - 1600 = 2400