Interpret Key Features from Linear Contexts

When Ashley left her house in the morning, her cell phone battery was partially charged. Let B represent the charge remaining in Ashley's battery, as a percentage, t hours since Ashley left her house. A graph of B is shown below.

Determine interpretation of the slope in the context of the problem.

• The slope represents the number of text messages sent by Ashley over time.
• The slope represents the amount of sunlight Ashley's phone is exposed to over time.
• The slope represents the distance Ashley traveled from her house over time.
• The slope represents the rate at which the battery charge is changing over time.

Micaela needs to lease out a music studio to record her new album. The studio charges an initial studio-use fee plus an hourly fee for each hour in the studio. Let P represent the total amount of money Micaela would have to pay to use the studio for t hours. A graph of P is shown below.

Determine the interpretation of the y-intercept in the context of the problem.

• The total price of using the studio for the day.

• The additional price per hour of using the studio.

• The total number of hours Micaela used the studio.

• The initial fee of using the stuido.

Adrian was given a box of assorted chocolates for his birthday. Each night, Adrian treats himself to some chocolates. Let C represent the number of chocolates remaining in the box t days after Adrian's birthday. A graph of C is shown below.

Determine the interpretation of the slope in the context of the problem.

• The number of chocolates in the original box.

• The number of chocolates Adrian eats each night.

• The number days after Adrian's birthday until all of the chocolates are gone.

• The total number of chocolates Adrian has eaten.

Fabian just lit a new candle and then let it burn all the way down to nothing. Let L represent the length of the candle remaining unburned, in inches, t hours after candle was lit. A graph of L is shown below.

Find the x-intercept of the graph and determine its interpretation in the context of the problem.

• The original length of the new candle.

• The number of inches of candle that burns per hour.

• The number of hours until the candle burned fully.

• The price of the candle.

An electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. Let C represent the total cost of the visit when the electrician spends t hours at the house working. A graph of C is shown.

Find the y-intercept of the graph and determine its interpretation in the context of the problem.

• The set fee for the house call.

• The hourly rate charged.

• The number of hours the electrician spends at the house.

• The total cost for all services.

Jack is going to use a computer at an internet cafe. The cafe charges an initial fee to use the computer and then an additional price per minute of usage. Let C represent the total cost of using a computer for t minutes at the internet cafe. A graph of C is shown below.

Identify the slope of the graph and determine its interpretation in the context of the problem.

• The number of minutes the computer was used.

• The total charge for using a computer.

• The additional charge per minute.

• The initial charge to use a computer.

Aubrey borrowed some money from her friend in order to help buy a new video game system. Aubrey agreed to pay the friend back some amount every week until her loan was paid off. Let L represent the amount Aubrey owes her friend after t weeks. A graph of L is shown below.

Identify the y-intercept of the graph and determine its interpretation in the context of the problem.

• The amount Aubrey borrowed from her friend.

• The price of the video game system.

• The number of weeks until the loan is paid off.

• The amount Aubrey paid back each week.

Ryan is in the business of manufacturing phones. He must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The equation C = 300 + 50p can be used to determine the total cost, in dollars, of producing p phones in a given day.

Identify the y-intercept of the equation and what is its interpretation in the context of the problem?

• The number of days to produce all of the phones.

• The additional coast to produce each phone.

• The total cost to produce all of the phones.

• The number of phones produced in a day.

• The fixed cost for rent and equipment.

Brayden was given a box of assorted chocolates for his birthday. Each night, Brayden treats himself to some chocolates. The number of chocolates remaining in the box t days after Brayden's birthday can be modeled by the equation C=−3t+12.

Identify the slope of the equation and what is its interpretation in the context of the problem?

• The number of days after Brayden's birthday until all of the chocolates are gone.

• The number of chocolates in the original box.

• The number of chocolates Brayden eats each night.

• The total number of chocolates Brayden has eaten.

Xavier filled up his car with gas before embarking on a road trip across the country. The number of gallons of gas remaining in his gas tank after t hours of driving can be determined using the equation G=12−0.75t. What is the x-intercept of the equation and what is its interpretation in the context of the problem?

• The number of gallons of gas used per hour driven.

• The number of hours driven until the tank is empty.

• The initial amount of gas in the tank.

• The number of galls of gas used per mile.