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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
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Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
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Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Who can show me the full solution in this problem?
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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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