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 $\text{\hspace{0.17em}}F\left(–40\right).$

what are you up to?
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
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
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
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
Jeffrey
Jeffrey
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?
which equation
Miranda
I dont know. lol
Jeffrey
Miranda
Jeffrey
answer and questions in exercise 11.2 sums
how do u calculate inequality of irrational number?
Alaba
give me an example
Chris
and I will walk you through it
Chris
cos (-z)= cos z .
cos(- z)=cos z
Mustafa
what is a algebra
(x+x)3=?
6x
Obed
what is the identity of 1-cos²5x equal to?
__john __05
Kishu
Hi
Abdel
hi
Ye
hi
Nokwanda
C'est comment
Abdel
Hi
Amanda
hello
SORIE
Hiiii
Chinni
hello
Ranjay
hi
ANSHU
hiiii
Chinni
h r u friends
Chinni
yes
Hassan
so is their any Genius in mathematics here let chat guys and get to know each other's
SORIE
I speak French
Abdel
okay no problem since we gather here and get to know each other
SORIE
hi im stupid at math and just wanna join here
Yaona
lol nahhh none of us here are stupid it's just that we have Fast, Medium, and slow learner bro but we all going to work things out together
SORIE
it's 12
what is the function of sine with respect of cosine , graphically
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
sinx sin2x is linearly dependent
what is a reciprocal
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
I don't understand how radicals works pls
How look for the general solution of a trig function