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.
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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.
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To graph a direct function:
1. Find 2 points which satisfy the equation
2. Plot them
3. Connect the points with a straight line
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
|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
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|