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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come graph a direct function:
1. Uncover 2 points which satisfy the equation
2. Plot them
3. Affix the points through a right line
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
|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
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|