The linear duty is renowned in economics. That is attractive due to the fact that it is an easy and simple to take care of mathematically. The has many important applications.
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Linear attributes are those whose graph is a straight line.
A linear function has the complying with form
y = f(x) = a + bx
A linear duty has one independent variable and also one dependence variable. The independent change is x and the dependent variable is y.
a is the continuous term or the y intercept. It is the worth of the dependence variable once x = 0.
b is the coefficient the the elevation variable. The is likewise known together the slope and also gives the rate of adjust of the dependence variable.
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come graph a linear function:
1. Find 2 point out which accomplish the equation
2. Plot them
3. Attach the points with a right line
Example:
y = 25 + 5x
let x = 1 then y = 25 + 5(1) = 30
let x = 3 then y = 25 + 5(3) = 40
A an easy example the a direct equation
A agency has fixed costs of $7,000 because that plant and also equuipment and also variable costs of $600 for each unit that output. What is total cost at varying levels the output?
let x = devices of calculation let C = full cost
C = fixed expense plus variable cost = 7,000 + 600 x
| output | total cost |
| 15 units | C = 7,000 + 15(600) = 16,000 |
| 30 devices | C = 7,000 + 30(600) = 25,000 |
Combinations of straight equations
Linear equations deserve to be included together, multiplied or divided.
A an easy example of enhancement of straight equations
C(x) is a price function
C(x) = fixed price + change cost
R(x) is a revenue function
R(x) = offering price (number of items sold)
profit equals revenue much 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 agency receives $45 for each unit of output sold. It has actually a variable cost of $25 every item and also a fixed expense of $1600. What is its benefit 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 |