# 4.1 Linear functions  (Page 16/27)

 Page 16 / 27

Write an equation for a line perpendicular to $\text{\hspace{0.17em}}h\left(t\right)=-2t+4\text{\hspace{0.17em}}$ and passing through the point $\text{\hspace{0.17em}}\left(-4,–1\right).$

Write an equation for a line perpendicular to $\text{\hspace{0.17em}}p\left(t\right)=3t+4\text{\hspace{0.17em}}$ and passing through the point $\text{\hspace{0.17em}}\left(3,1\right).$

$y=-\frac{1}{3}t+2$

## Graphical

For the following exercises, find the slope of the line graphed.

0

For the following exercises, write an equation for the line graphed.

$y=-\frac{5}{4}x+5$

$y=3x-1$

$y=-2.5$

For the following exercises, match the given linear equation with its graph in [link] .

$f\left(x\right)=-x-1$

$f\left(x\right)=-2x-1$

F

$f\left(x\right)=-\frac{1}{2}x-1$

$f\left(x\right)=2$

C

$f\left(x\right)=2+x$

$f\left(x\right)=3x+2$

A

For the following exercises, sketch a line with the given features.

An x -intercept of $\text{\hspace{0.17em}}\left(–4,\text{0}\right)\text{\hspace{0.17em}}$ and y -intercept of $\text{\hspace{0.17em}}\left(0,\text{–2}\right)$

An x -intercept $\text{\hspace{0.17em}}\left(–2,\text{0}\right)\text{\hspace{0.17em}}$ and y -intercept of $\text{\hspace{0.17em}}\left(0,\text{4}\right)$

A y -intercept of $\text{\hspace{0.17em}}\left(0,\text{7}\right)\text{\hspace{0.17em}}$ and slope $\text{\hspace{0.17em}}-\frac{3}{2}$

A y -intercept of $\text{\hspace{0.17em}}\left(0,\text{3}\right)\text{\hspace{0.17em}}$ and slope $\text{\hspace{0.17em}}\frac{2}{5}$

Passing through the points $\text{\hspace{0.17em}}\left(–6,\text{–2}\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(6,\text{–6}\right)$

Passing through the points $\text{\hspace{0.17em}}\left(–3,\text{–4}\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(3,\text{0}\right)$

For the following exercises, sketch the graph of each equation.

$f\left(x\right)=-2x-1$

$f\left(x\right)=-3x+2$

$f\left(x\right)=\frac{1}{3}x+2$

$f\left(x\right)=\frac{2}{3}x-3$

$f\left(t\right)=3+2t$

$p\left(t\right)=-2+3t$

$x=3$

$x=-2$

$r\left(x\right)=4$

For the following exercises, write the equation of the line shown in the graph.

$y=\text{3}$

$x=-3$

## Numeric

For the following exercises, which of the tables could represent a linear function? For each that could be linear, find a linear equation that models the data.

 $x$ 0 5 10 15 $g\left(x\right)$ 5 –10 –25 –40

Linear, $\text{\hspace{0.17em}}g\left(x\right)=-3x+5$

 $x$ 0 5 10 15 $h\left(x\right)$ 5 30 105 230
 $x$ 0 5 10 15 $f\left(x\right)$ –5 20 45 70

Linear, $\text{\hspace{0.17em}}f\left(x\right)=5x-5$

 $x$ 5 10 20 25 $k\left(x\right)$ 13 28 58 73
 $x$ 0 2 4 6 $g\left(x\right)$ 6 –19 –44 –69

Linear, $\text{\hspace{0.17em}}g\left(x\right)=-\frac{25}{2}x+6$

 $x$ 2 4 8 10 $h\left(x\right)$ 13 23 43 53
 $x$ 2 4 6 8 $f\left(x\right)$ –4 16 36 56

Linear, $\text{\hspace{0.17em}}f\left(x\right)=10x-24$

 $x$ 0 2 6 8 $k\left(x\right)$ 6 31 106 231

## Technology

For the following exercises, use a calculator or graphing technology to complete the task.

If $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ is a linear function, find an equation for the function.

$f\left(x\right)=-58x+17.3$

Graph the function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ on a domain of $\text{\hspace{0.17em}}\left[–10,10\right]:f\left(x\right)=0.02x-0.01.\text{\hspace{0.17em}}$ Enter the function in a graphing utility. For the viewing window, set the minimum value of $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ to be $\text{\hspace{0.17em}}-10\text{\hspace{0.17em}}$ and the maximum value of $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ to be $\text{\hspace{0.17em}}10.$

Graph the function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ on a domain of $\text{\hspace{0.17em}}\left[–10,10\right]:fx\right)=2,500x+4,000$

[link] shows the input, $\text{\hspace{0.17em}}w,$ and output, $\text{\hspace{0.17em}}k,$ for a linear function $\text{\hspace{0.17em}}k.\text{\hspace{0.17em}}$ a. Fill in the missing values of the table. b. Write the linear function $\text{\hspace{0.17em}}k,$ round to 3 decimal places.

 w –10 5.5 67.5 b k 30 –26 a –44

[link] shows the input, $\text{\hspace{0.17em}}p,$ and output, $\text{\hspace{0.17em}}q,$ for a linear function $\text{\hspace{0.17em}}q.\text{\hspace{0.17em}}$ a. Fill in the missing values of the table. b. Write the linear function $\text{\hspace{0.17em}}k.$

 p 0.5 0.8 12 b q 400 700 a 1,000,000

Graph the linear function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ on a domain of $\text{\hspace{0.17em}}\left[-10,10\right]\text{\hspace{0.17em}}$ for the function whose slope is $\text{\hspace{0.17em}}\frac{1}{8}\text{\hspace{0.17em}}$ and y -intercept is $\text{\hspace{0.17em}}\frac{31}{16}.\text{\hspace{0.17em}}$ Label the points for the input values of $\text{\hspace{0.17em}}-10\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}10.$

Graph the linear function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ on a domain of $\text{\hspace{0.17em}}\left[-0.1,0.1\right]\text{\hspace{0.17em}}$ for the function whose slope is 75 and y -intercept is $\text{\hspace{0.17em}}-22.5.\text{\hspace{0.17em}}$ Label the points for the input values of $\text{\hspace{0.17em}}-0.1\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}0.1.$

Graph the linear function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ where $\text{\hspace{0.17em}}f\left(x\right)=ax+b\text{\hspace{0.17em}}$ on the same set of axes on a domain of $\text{\hspace{0.17em}}\left[-4,4\right]\text{\hspace{0.17em}}$ for the following values of $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}b.$

1. $a=2;b=3$
2. $a=2;b=4$
3. $a=2;b=–4$
4. $a=2;b=–5$

## Extensions

Find the value of $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ if a linear function goes through the following points and has the following slope: $\text{\hspace{0.17em}}\left(x,2\right),\left(-4,6\right),\text{\hspace{0.17em}}m=3$

Find the value of y if a linear function goes through the following points and has the following slope: $\text{\hspace{0.17em}}\left(10,y\right),\left(25,100\right),\text{\hspace{0.17em}}m=-5$

y = 175

#### Questions & Answers

what are you up to?
Mark Reply
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
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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
answer and questions in exercise 11.2 sums
Yp Reply
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 .
Swadesh
cos(- z)=cos z
Mustafa
what is a algebra
Jallah Reply
(x+x)3=?
Narad
6x
Obed
what is the identity of 1-cos²5x equal to?
liyemaikhaya Reply
__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
Karl Reply
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
Aashish Reply
sinx sin2x is linearly dependent
cr Reply
what is a reciprocal
Ajibola Reply
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
Funmilola Reply
I don't understand how radicals works pls
Kenny Reply
How look for the general solution of a trig function
collins Reply

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