The linear function is renowned in economics. It is attractive since it is straightforward and straightforward to handle mathematically. It has numerous important applications.

You are watching: Characteristics of linear functions

Linear features are those whose graph is a directly line.

A linear duty has the adhering to form

y = f(x) = a + bx

A linear function has one elevation variable and also one dependency variable. The independent variable is x and also the dependent change is y.

a is the constant term or the y intercept. It is the worth of the dependent variable as soon as x = 0.

b is the coefficient the the live independence variable. It is also known together the slope and gives the price of adjust of the dependency variable.

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**Graphing a direct function**

come graph a direct function:

1. Uncover 2 points which satisfy the equation

2. Plot them

3. Affix the points through a right line

**Example: **

y = 25 + 5x

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

let x = 3 then y = 25 + 5(3) = 40

**A basic example that a linear equation**

A firm has fixed expenses of $7,000 because that plant and equuipment and also variable costs of $600 because that each unit of output. What is total cost at differing levels the output?

let x = devices of output let C = full cost

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

output | total cost |

15 devices | C = 7,000 + 15(600) = 16,000 |

30 devices | C = 7,000 + 30(600) = 25,000 |

**Combinations of straight equations**

Linear equations can be added together, multiply or divided.

**A simple example of enhancement of linear equations**

C(x) is a price function

C(x) = fixed expense + change cost

R(x) is a revenue function

R(x) = offering price (number of item sold)

profit equals revenue less cost

P(x) is a profit function

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

x = the variety of items produced and also sold

**Data:**

A company receives $45 for each unit of calculation sold. It has a variable price of $25 every item and also a fixed cost of $1600. What is its profit if the 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 |