Writing and graphing Equations in Two Variables

Which graph shows the equation V = 4 + 2t, where V is the total volume of water in a bucket and t is the elapsed time in minutes?

C

Which graph represents viable values for y = 2x, where x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of the rice?

A

Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which best describes why the graph relating the total amount of gasoline in the tank, y, to the number of gallons that she added to it, x, will be continuous or discrete?

The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.

Diep bought a baguette loaf of bread 65 centimeters long. For lunch every afternoon, he cuts 15 centimeters of bread for his sandwich. Diep wants to determine the length of the loaf of bread, l, after d days. What is the equation of the scenario? Is the graph of the equation continuous or discrete?

l = 65 - 15d; discrete

Which scenario is most likely the one shown on the graph?

the total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce

Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?

(8, 2.40)

Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces. Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?

(0, 0)

Which description is represented by a discrete graph?

Kiley bought a platter for $19 and several matching bowls that were $8 each. What is the total cost before tax?

A store sells notebooks for $3 each and does not charge sales tax. If x represents the number of notebooks Adele buys and y represents the total cost of the notebooks she buys, which best describes the values of x and y?

The value of x can be any integer greater than or equal to 0, and y will be an integer greater than or equal to 0.

The graph shows the relationship between the number of minutes Maria spent jogging on a treadmill and the distance she jogged. What was her speed?

0.1 mile per minute

Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?

B

The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination. Which statement is true?

For each hour that Michelle drove, she traveled an additional 50 miles.

The yearbook club has 5 members returning from last year. They set up a booth in the cafeteria to recruit more members, and an average of 3 new members sign up each day. Which best describes why the graph relating the total number of members on the yearbook club, m, and the number of days the booth is set up, d, will be continuous or discrete?

The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups.

Peaches are being sold for $2 per pound. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y?

The values of both x and y will be real numbers greater than or equal to 0.

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let y represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, t? Is the graph of the equation continuous or discrete?

t=4y+7.75; continuous

The graph shows the relationship between the total cost and the number of gift cards that Raj bought for raffle prizes. What would be the cost for 5 of the gift cards?

$100

The graph below shows the amount of money left in the school's desk fund, f, after d desks have been purchased. For each new desk that is purchased, by how much does the amount of money left in the school's desk fund decrease?

110

Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. What is the equation that can be used to find the value of y, the total time that Vlad spent on his homework, and what are the constraints on the values of x and y?

y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.

Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?

y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.