# 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

bsc F. y algebra and trigonometry pepper 2
Aditi Reply
given that x= 3/5 find sin 3x
Adamu Reply
4
DB
remove any signs and collect terms of -2(8a-3b-c)
Joeval Reply
-16a+6b+2c
Will
is that a real answer
Joeval
(x2-2x+8)-4(x2-3x+5)
Ayush Reply
sorry
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
(X2-2X+8)-4(X2-3X+5)=0 ?
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
Y
master
X2-2X+8-4X2+12X-20=0 (X2-4X2)+(-2X+12X)+(-20+8)= 0 -3X2+10X-12=0 3X2-10X+12=0 Use quadratic formula To find the answer answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x2-2x+8-4x2+12x-20 x2-4x2-2x+12x+8-20 -3x2+10x-12 now you can find the answer using quadratic
Mukhtar
explain and give four example of hyperbolic function
Lukman Reply
What is the correct rational algebraic expression of the given "a fraction whose denominator is 10 more than the numerator y?
Racelle Reply
y/y+10
Mr
Find nth derivative of eax sin (bx + c).
Anurag Reply
Find area common to the parabola y2 = 4ax and x2 = 4ay.
Anurag
A rectangular garden is 25ft wide. if its area is 1125ft, what is the length of the garden
Jhovie Reply
to find the length I divide the area by the wide wich means 1125ft/25ft=45
Miranda
thanks
Jhovie
What do you call a relation where each element in the domain is related to only one value in the range by some rules?
Charmaine Reply
A banana.
Yaona
given 4cot thither +3=0and 0°<thither <180° use a sketch to determine the value of the following a)cos thither
Snalo Reply
what are you up to?
Mark Reply
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
aap konsi country se ho
jai
which language is that
Miranda
I am living in india
jai
good
Miranda
what is the formula for calculating algebraic
Propessor Reply
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
state and prove Cayley hamilton therom
sita Reply
hello
Propessor
hi
Miranda
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.
Miranda
hi
jai
hi Miranda
jai
thanks
Propessor
welcome
jai
What is algebra
Pearl Reply
algebra is a branch of the mathematics to calculate expressions follow.
Miranda
Miranda Drice would you mind teaching me mathematics? I think you are really good at math. I'm not good at it. In fact I hate it. 😅😅😅
Jeffrey
lolll who told you I'm good at it
Miranda
something seems to wispher me to my ear that u are good at it. lol
Jeffrey
lolllll if you say so
Miranda
but seriously, Im really bad at math. And I hate it. But you see, I downloaded this app two months ago hoping to master it.
Jeffrey
which grade are you in though
Miranda
oh woww I understand
Miranda
haha. already finished college
Jeffrey
how about you? what grade are you now?
Jeffrey
I'm going to 11grade
Miranda
how come you finished in college and you don't like math though
Miranda
gotta practice, holmie
Steve
if you never use it you won't be able to appreciate it
Steve
I don't know why. But Im trying to like it.
Jeffrey
yes steve. you're right
Jeffrey
so you better
Miranda
what is the solution of the given equation?
Nelson Reply
which equation
Miranda
I dont know. lol
Jeffrey
please where is the equation
Miranda
ask nelson. lol
Jeffrey

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