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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

What are the factors that affect demand for a commodity
Florence Reply
differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
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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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