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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 value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
hi vedant can u help me with some assignments
Solomon
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma

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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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