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The equation P = 31 + 1.75 w models the relation between the amount of Tuyet’s monthly water bill payment, P , in dollars, and the number of units of water, w , used.

  1. Find Tuyet’s payment for a month when 0 units of water are used.
  2. Find Tuyet’s payment for a month when 12 units of water are used.
  3. Interpret the slope and P -intercept of the equation.
  4. Graph the equation.
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The equation P = 28 + 2.54 w models the relation between the amount of Randy’s monthly water bill payment, P , in dollars, and the number of units of water, w , used.

  1. Find the payment for a month when Randy used 0 units of water.
  2. Find the payment for a month when Randy used 15 units of water.
  3. Interpret the slope and P -intercept of the equation.
  4. Graph the equation.
  1. $28
  2. $66.10
  3. The slope, 2.54, means that Randy’s payment, P , increases by $2.54 when the number of units of water he used, w, increases by 1. The P –intercept means that if the number units of water Randy used was 0, the payment would be $28.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).

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Bruce drives his car for his job. The equation R = 0.575 m + 42 models the relation between the amount in dollars, R , that he is reimbursed and the number of miles, m , he drives in one day.

  1. Find the amount Bruce is reimbursed on a day when he drives 0 miles.
  2. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
  3. Interpret the slope and R -intercept of the equation.
  4. Graph the equation.
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Janelle is planning to rent a car while on vacation. The equation C = 0.32 m + 15 models the relation between the cost in dollars, C , per day and the number of miles, m , she drives in one day.

  1. Find the cost if Janelle drives the car 0 miles one day.
  2. Find the cost on a day when Janelle drives the car 400 miles.
  3. Interpret the slope and C –intercept of the equation.
  4. Graph the equation.
  1. $15
  2. $143
  3. The slope, 0.32, means that the cost, C , increases by $0.32 when the number of miles driven, m, increases by 1. The C -intercept means that if Janelle drives 0 miles one day, the cost would be $15.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).

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Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation S = 400 + 0.15 c models the relation between her weekly salary, S , in dollars and the amount of her sales, c , in dollars.

  1. Find Cherie’s salary for a week when her sales were 0.
  2. Find Cherie’s salary for a week when her sales were 3600.
  3. Interpret the slope and S –intercept of the equation.
  4. Graph the equation.
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Patel’s weekly salary includes a base pay plus commission on his sales. The equation S = 750 + 0.09 c models the relation between his weekly salary, S , in dollars and the amount of his sales, c , in dollars.

  1. Find Patel’s salary for a week when his sales were 0.
  2. Find Patel’s salary for a week when his sales were 18,540.
  3. Interpret the slope and S -intercept of the equation.
  4. Graph the equation.
  1. $750
  2. $2418.60
  3. The slope, 0.09, means that Patel’s salary, S , increases by $0.09 for every $1 increase in his sales. The S -intercept means that when his sales are $0, his salary is $750.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).

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Costa is planning a lunch banquet. The equation C = 450 + 28 g models the relation between the cost in dollars, C , of the banquet and the number of guests, g .

  1. Find the cost if the number of guests is 40.
  2. Find the cost if the number of guests is 80.
  3. Interpret the slope and C -intercept of the equation.
  4. Graph the equation.
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Margie is planning a dinner banquet. The equation C = 750 + 42 g models the relation between the cost in dollars, C of the banquet and the number of guests, g .

  1. Find the cost if the number of guests is 50.
  2. Find the cost if the number of guests is 100.
  3. Interpret the slope and C –intercept of the equation.
  4. Graph the equation.
  1. $2850
  2. $4950
  3. The slope, 42, means that the cost, C , increases by $42 for when the number of guests increases by 1. The C -intercept means that when the number of guests is 0, the cost would be $750.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).

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Use Slopes to Identify Parallel Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.

y = 3 4 x 3 ; 3 x 4 y = 2

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y = 2 3 x 1 ; 2 x 3 y = 2

parallel

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2 x 5 y = 3 ; y = 2 5 x + 1

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3 x 4 y = 2 ; y = 3 4 x 3

parallel

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2 x 4 y = 6 ; x 2 y = 3

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6 x 3 y = 9 ; 2 x y = 3

not parallel

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4 x + 2 y = 6 ; 6 x + 3 y = 3

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8 x + 6 y = 6 ; 12 x + 9 y = 12

parallel

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x = 7 ; x = 8

parallel

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x = 3 ; x = 2

parallel

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y = 1 ; y = 2

parallel

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x y = 2 ; 2 x 2 y = 4

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4 x + 4 y = 8 ; x + y = 2

not parallel

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x 3 y = 6 ; 2 x 6 y = 12

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5 x 2 y = 11 ; 5 x y = 7

not parallel

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3 x 6 y = 12 ; 6 x 3 y = 3

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4 x 8 y = 16 ; x 2 y = 4

not parallel

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9 x 3 y = 6 ; 3 x y = 2

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x 5 y = 10 ; 5 x y = 10

not parallel

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7 x 4 y = 8 ; 4 x + 7 y = 14

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9 x 5 y = 4 ; 5 x + 9 y = 1

not parallel

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Use Slopes to Identify Perpendicular Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.

3 x 2 y = 8 ; 2 x + 3 y = 6

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x 4 y = 8 ; 4 x + y = 2

perpendicular

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2 x + 5 y = 3 ; 5 x 2 y = 6

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2 x + 3 y = 5 ; 3 x 2 y = 7

perpendicular

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3 x 2 y = 1 ; 2 x 3 y = 2

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3 x 4 y = 8 ; 4 x 3 y = 6

not perpendicular

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5 x + 2 y = 6 ; 2 x + 5 y = 8

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2 x + 4 y = 3 ; 6 x + 3 y = 2

not perpendicular

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4 x 2 y = 5 ; 3 x + 6 y = 8

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2 x 6 y = 4 ; 12 x + 4 y = 9

perpendicular

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6 x 4 y = 5 ; 8 x + 12 y = 3

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8 x 2 y = 7 ; 3 x + 12 y = 9

perpendicular

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Everyday math

The equation C = 5 9 F 17.8 can be used to convert temperatures F , on the Fahrenheit scale to temperatures, C , on the Celsius scale.

  1. Explain what the slope of the equation means.
  2. Explain what the C –intercept of the equation means.
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The equation n = 4 T 160 is used to estimate the number of cricket chirps, n , in one minute based on the temperature in degrees Fahrenheit, T .

  1. Explain what the slope of the equation means.
  2. Explain what the n –intercept of the equation means. Is this a realistic situation?
  1. For every increase of one degree Fahrenheit, the number of chirps increases by four.
  2. There would be −160 chirps when the Fahrenheit temperature is 0 ° . (Notice that this does not make sense; this model cannot be used for all possible temperatures.)
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Writing exercises

Explain in your own words how to decide which method to use to graph a line.

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Why are all horizontal lines parallel?

Answers will vary.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has eight rows and four columns. The first row is a header row and it labels each column. The first column is labeled

After looking at the checklist, do you think you are well-prepared for the next section? Why or why not?

Questions & Answers

the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
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Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
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cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
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Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
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life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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