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Write an equation for a line perpendicular to h ( t ) = −2 t + 4 and passing through the point ( −4 , –1 ) .

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Write an equation for a line perpendicular to p ( t ) = 3 t + 4 and passing through the point ( 3 , 1 ) .

y = 1 3 t + 2

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Graphical

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

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

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

Graph of six functions where line A has a slope of 3 and y-intercept at 2, line B has a slope of 1 and y-intercept at 2, line C has a slope of 0 and y-intercept at 2, line D has a slope of -1/2 and y-intercept at -1, line E has a slope of -1 and y-intercept at -1, and line F has a slope of -2 and y-intercept at -1.

f ( x ) = −2 x 1

F

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f ( x ) = 1 2 x 1

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

An x -intercept of ( –4 , 0 ) and y -intercept of ( 0 , –2 )

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An x -intercept ( –2 , 0 ) and y -intercept of ( 0 , 4 )

Graph of f with an x-intercept at -4 and y-intercept at -2 which gives us a slope of: 2.
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A y -intercept of ( 0 , 7 ) and slope 3 2

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A y -intercept of ( 0 , 3 ) and slope 2 5

Graph of f with an y-intercept at 3 and a slope of 2/5.
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Passing through the points ( –6 , –2 ) and ( 6 , –6 )

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Passing through the points ( –3 , –4 ) and ( 3 , 0 )

Graph of a line that passes through the points (-3, -4) and (3, 0) which results in a slope of 2/3.
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For the following exercises, sketch the graph of each equation.

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

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 ( x ) 5 –10 –25 –40

Linear, g ( x ) = 3 x + 5

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

Linear, f ( x ) = 5 x 5

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

Linear, g ( x ) = 25 2 x + 6

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

Linear, f ( x ) = 10 x 24

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x 0 2 6 8
k ( x ) 6 31 106 231
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Technology

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

If f is a linear function, f ( 0.1 ) = 11.5 ,   and   f ( 0.4 ) = –5.9 , find an equation for the function.

f ( x ) = 58 x + 17.3

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Graph the function f on a domain of [ –10 , 10 ] : f ( x ) = 0.02 x 0.01. Enter the function in a graphing utility. For the viewing window, set the minimum value of x to be −10 and the maximum value of x to be 10.

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Graph the function f on a domain of [ –10 , 10 ] : f x ) = 2 , 500 x + 4 , 000

Graph of f(x) = 2500x + 4000
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[link] shows the input, w , and output, k , for a linear function k . a. Fill in the missing values of the table. b. Write the linear function k , round to 3 decimal places.

w –10 5.5 67.5 b
k 30 –26 a –44

y = 3.613 x 6.129  

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[link] shows the input, p , and output, q , for a linear function q . a. Fill in the missing values of the table. b. Write the linear function k .

p 0.5 0.8 12 b
q 400 700 a 1,000,000
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Graph the linear function f on a domain of [ 10 , 10 ] for the function whose slope is 1 8 and y -intercept is 31 16 . Label the points for the input values of −10 and 10.

Graph of a line with endpoints at (-10, 0.6875) and (10, 3.1875).
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Graph the linear function f on a domain of [ 0.1 , 0.1 ] for the function whose slope is 75 and y -intercept is −22.5. Label the points for the input values of −0.1 and 0.1.

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Graph the linear function f where f ( x ) = a x + b on the same set of axes on a domain of [ 4 , 4 ] for the following values of a and b .

  1. a = 2 ; b = 3
  2. a = 2 ; b = 4
  3. a = 2 ; b = –4
  4. a = 2 ; b = –5
Graph of four functions where the blue line is f(x) = 2x+4 which has a slope of 2 and y-intercept of 4, the orange line is f(x) = 2x +3 which has a slope of 2 and a y-intercept of 3, the turquoise line is f(x) = 2x – 4 which has a slope of 2 and a y-intercept of -4, and the red line is f(x) = 2x -5 which has a slope of 2 and a y-intercept of -5.
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Extensions

Find the value of x if a linear function goes through the following points and has the following slope: ( x , 2 ) , ( −4 , 6 ) , m = 3

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Find the value of y if a linear function goes through the following points and has the following slope: ( 10 , y ) , ( 25 , 100 ) , m = −5

y = 175

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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
new member
siame
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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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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