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- College algebra
- Linear functions
- Modeling with linear functions
Key concepts
- We can use the same problem strategies that we would use for any type of function.
- When modeling and solving a problem, identify the variables and look for key values, including the slope and
y -intercept. See
[link] .
- Draw a diagram, where appropriate. See
[link] and
[link] .
- Check for reasonableness of the answer.
- Linear models may be built by identifying or calculating the slope and using the
y -intercept.
- The
x -intercept may be found by setting
which is setting the expression
equal to 0.
- The point of intersection of a system of linear equations is the point where the
x - and
y -values are the same. See
[link] .
- A graph of the system may be used to identify the points where one line falls below (or above) the other line.
Section exercises
Verbal
Explain how to find the input variable in a word problem that uses a linear function.
Determine the independent variable. This is the variable upon which the output depends.
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Explain how to interpret the initial value in a word problem that uses a linear function.
To determine the initial value, find the output when the input is equal to zero.
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Algebraic
Find the area of a parallelogram bounded by the
y -axis, the line
the line
and the line parallel to
passing through
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Find the area of a parallelogram bounded by the
x -axis, the line
the line
and the line parallel to
passing through
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For the following exercises, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped 4,700. Assume this trend continues.
For the following exercises, consider this scenario: A town’s population has been increased at a constant rate. In 2010 the population was 46,020. By 2012 the population had increased to 52,070. Assume this trend continues.
For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years.
Find the linear function that models the town’s population
as a function of the year,
where
is the number of years since the model began.
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If the function
is graphed, find and interpret the
x - and
y -intercepts.
(–30, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.
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Questions & Answers
If c is the cost function for a particular product, find the marginal cost functions and their
values at x=10 a. c(x) = 800+ 0.04x + 0.0002x² b. c(x) = 250 + 100x + 0.001x²
how can I find set theory
how can I find set theory
Jarvis
is there an error on the one about the dime's thickness? says 2.2x10⁶=0.00135 m
hi, interested in algebra
how to reduce an equation?
Makan
by manipulation of both side
Al
9(y+8)-27 is 9y+45.
Why can't you reduce that to y+5? I know that's wrong but can't explain why
when you reduce an equation to its simplest terms, you can't change the value of the equation. reducing it to y + 5 is equivalent to dividing it by 9 which changes the value. you can multiply it by 1 or 9/9 which would give 9(y + 5). multiplying it by one does not change the value.
Philip
Given a polynomial expression, factor out the greatest common factor.
WHAT IS QUADRATIC EQUATION?
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
what are equations?
Charles
Definition of economics according to
karl Marx
Thomas malthus
Jeremy bentham
David Ricardo
J.K
Rakiya
Please help me is assignment
Rakiya
The 47th problem of Euclid
Kenneth
show that the set of all natural number form semi group under the composition of addition
what is the meaning
Dominic
explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the
fraction, the value of the fraction becomes 2/3. Find the original fraction.
2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2
-------------- = _
x + 9 + 6 3
x + 6 3
----------- x -- (cross multiply)
x + 15 2
3(x + 6) = 2(x + 15)
3x + 18 = 2x + 30 (-2x from both)
x + 18 = 30 (-18 from both)
x = 12
Test:
12 + 6 18 2
-------------- = --- = ---
12 + 9 + 6 27 3
Pawel
2.
(x) + (x + 2) = 60
2x + 2 = 60
2x = 58
x = 29
29, 30, & 31
Pawel
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Q2
x+(x+2)+(x+4)=60
3x+6=60
3x+6-6=60-6
3x=54
3x/3=54/3
x=18
:. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1
x + 3x + 1 = 113
4x = 112, x = 28
Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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