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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

show that the set of all natural number form semi group under the composition of addition
Nikhil Reply
explain and give four Example hyperbolic function
Lukman Reply
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
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
yes i wantt to review
Mark
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
please help me prove quadratic formula
Darius
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
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
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

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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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