# 4.1 Linear functions  (Page 17/27)

 Page 17 / 27

Find the equation of the line that passes through the following points:

and

Find the equation of the line that passes through the following points:

$\left(2a,b\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(a,b+1\right)$

$y=-\frac{1}{2}x+b+2$

Find the equation of the line that passes through the following points:

$\left(a,0\right)$ and $\text{\hspace{0.17em}}\left(c,d\right)$

Find the equation of the line parallel to the line $\text{\hspace{0.17em}}g\left(x\right)=-0.\text{01}x\text{+2}\text{.01}\text{\hspace{0.17em}}$ through the point $\text{\hspace{0.17em}}\left(1,\text{2}\right).$

y = –0.01 x + 2.01

Find the equation of the line perpendicular to the line $\text{\hspace{0.17em}}g\left(x\right)=-0.\text{01}x\text{+2}\text{.01}\text{\hspace{0.17em}}$ through the point $\text{\hspace{0.17em}}\left(1,\text{2}\right).$

For the following exercises, use the functions

Find the point of intersection of the lines $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}g.$

Where is $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ greater than $\text{\hspace{0.17em}}g\left(x\right)?\text{\hspace{0.17em}}$ Where is $\text{\hspace{0.17em}}g\left(x\right)\text{\hspace{0.17em}}$ greater than $\text{\hspace{0.17em}}f\left(x\right)?$

## Real-world applications

At noon, a barista notices that she has $20 in her tip jar. If she makes an average of$0.50 from each customer, how much will she have in her tip jar if she serves $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ more customers during her shift?

$20+0.5n$

A gym membership with two personal training sessions costs $125, while gym membership with five personal training sessions costs$260. What is cost per session?

A clothing business finds there is a linear relationship between the number of shirts, $\text{\hspace{0.17em}}n,$ it can sell and the price, $\text{\hspace{0.17em}}p,$ it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $\text{\hspace{0.17em}}30,$ while 3,000 shirts can be sold at a price of $22. Find a linear equation in the form $\text{\hspace{0.17em}}p\left(n\right)=mn+b\text{\hspace{0.17em}}$ that gives the price $\text{\hspace{0.17em}}p\text{\hspace{0.17em}}$ they can charge for $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ shirts. $p\left(n\right)=-0.004n+34$ A phone company charges for service according to the formula: $\text{\hspace{0.17em}}C\left(n\right)=24+0.1n,$ where $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ is the number of minutes talked, and $\text{\hspace{0.17em}}C\left(n\right)\text{\hspace{0.17em}}$ is the monthly charge, in dollars. Find and interpret the rate of change and initial value. A farmer finds there is a linear relationship between the number of bean stalks, $\text{\hspace{0.17em}}n,$ she plants and the yield, $\text{\hspace{0.17em}}y,$ each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Find a linear relationships in the form $\text{\hspace{0.17em}}y=mn+b\text{\hspace{0.17em}}$ that gives the yield when $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ stalks are planted. $y=-0.5n+45$ A city’s population in the year 1960 was 287,500. In 1989 the population was 275,900. Compute the rate of growth of the population and make a statement about the population rate of change in people per year. A town’s population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. Write an equation, $\text{\hspace{0.17em}}P\left(t\right),$ for the population $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ years after 2003. $P\left(t\right)=1700t+45,000$ Suppose that average annual income (in dollars) for the years 1990 through 1999 is given by the linear function: $\text{\hspace{0.17em}}I\left(x\right)=1054x+23,286,$ where $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ is the number of years after 1990. Which of the following interprets the slope in the context of the problem? 1. As of 1990, average annual income was$23,286.
2. In the ten-year period from 1990–1999, average annual income increased by a total of $1,054. 3. Each year in the decade of the 1990s, average annual income increased by$1,054.
4. Average annual income rose to a level of \$23,286 by the end of 1999.

When temperature is 0 degrees Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the corresponding Fahrenheit temperature is 212. Express the Fahrenheit temperature as a linear function of $\text{\hspace{0.17em}}C,$ the Celsius temperature, $\text{\hspace{0.17em}}F\left(C\right).$

1. Find the rate of change of Fahrenheit temperature for each unit change temperature of Celsius.
2. Find and interpret $\text{\hspace{0.17em}}F\left(28\right).$
3. Find and interpret $\text{\hspace{0.17em}}F\left(–40\right).$

#### Questions & Answers

Find the possible value of 8.5 using moivre's theorem
Reuben Reply
which of these functions is not uniformly cintinuous on (0, 1)? sinx
Pooja Reply
which of these functions is not uniformly continuous on 0,1
Basant Reply
solve this equation by completing the square 3x-4x-7=0
Jamiz Reply
X=7
Muustapha
=7
mantu
x=7
mantu
3x-4x-7=0 -x=7 x=-7
Kr
x=-7
mantu
9x-16x-49=0 -7x=49 -x=7 x=7
mantu
what's the formula
Modress
-x=7
Modress
what is trigonometry
Jean Reply
deals with circles, angles, and triangles. Usually in the form of Soh cah toa or sine, cosine, and tangent
Thomas
solve for me this equational y=2-x
Rubben Reply
what are you solving for
Alex
solve x
Rubben
you would move everything to the other side leaving x by itself. subtract 2 and divide -1.
Nikki
then I got x=-2
Rubben
it will b -y+2=x
Alex
goodness. I'm sorry. I will let Alex take the wheel.
Nikki
ouky thanks braa
Rubben
I think he drive me safe
Rubben
how to get 8 trigonometric function of tanA=0.5, given SinA=5/13? Can you help me?m
Pab Reply
More example of algebra and trigo
Stephen Reply
What is Indices
Yashim Reply
If one side only of a triangle is given is it possible to solve for the unkown two sides?
Felix Reply
cool
Rubben
kya
Khushnama
please I need help in maths
Dayo Reply
Okey tell me, what's your problem is?
Navin
the least possible degree ?
Dejen Reply
(1+cosA)(1-cosA)=sin^2A
BINCY Reply
good
Neha
why I'm sending you solved question
Mirza
Teach me abt the echelon method
Khamis
exact value of cos(π/3-π/4)
Ankit Reply
What is differentiation?
Intakhab Reply

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