Interpreting Expressions in Context

The value of property in a particular area depends on the land and the square footage of the house according to the equation given below, where x represents the square footage of the house, in square feet.

V=80x+6000

What is the meaning of the Y-intercept and slope in this context?

• The Y-intercept is the value of the house not including the land, and the slope is the rate of increase of the value of the house for each increase in square footage.

• The Y-intercept is the value of the house not including the land, and the slope is the total value of the house and land.

• The Y-intercept is the total value of the house and land, and the slope is the value of the house not including the land.

• The Y-intercept is the rate of increase of the value of the house for each increase in square footage, and the slope is the value of the land without the house.

Jada is traveling to her college, which is 75 miles from her home, at a speed of 30 miles per hour. Which equation best represents the distance remaining to the college after x hours, and why?

• f(x)=75(0.70)^x; the function is exponential because the distance to the college decreases by a constant percentage each hour
• f(x)=75(1.30)^x; the function is exponential because the distance to the college increases by a constant percentage each hour
• f(x)=75-30x; the function is linear because the distance to the college decreases by a constant rate each hour
• f(x)=75+30x; the function is linear because the distance to the college increases by a constant rate each hour

Jerami is going to deposit an equal amount of money into a checking account each month until he has saved $2,000. The amount of money, y, in the account after x months can be modeled by the equation y=35x+250. What does the slope of the graph of the equation represent?

• The amount of money deposited monthly.
• The amount of money originally in the account.
• The number of months it would take to earn $250.
• The number of months it would take to reach $2,000.

Dan's football team brings a 5-gallon cooler of Powerade to every game so players can stay hydrated. The amount of Powerade in the cooler can be modeled by the equation y=5-0.2x, where y is the amount of Powerade in the cooler in gallons, and x is the number of players who have taken a drink of Powerade. Which best describes the amount, in gallons, of Powerade that is in the cooler at any time, x?

• The amount of Powerade in the cooler decreases at a constant rate.
• The amount of Powerade in the cooler increases at a constant rate.
• The amount of Powerade in the cooler decreases at an exponential rate.
• The amount of Powerade in the cooler increases at an exponential rate.

A company’s rate of growth is represented by the equation y=0.5x+2500. Which statement about the company’s growth is true?

• The company has an inconsistent rate of growth.
• The company has an exponential rate of growth.
• The company has a constant rate of growth.
• The company has a nonexistent rate of growth.

The owner of a small computer repair business has one employee, who is paid an hourly rate of $22. The owner estimates his weekly profit using the function P(x) = -22x+8600. In this function, x represents the number of

• computers repaired per week
• hours worked per week
• customers served per week
• days worked per week

To which of the following situations can the function y = 5x+10 best be applied?

• The number of miles a person walks if he walks for 5 hours at the rate of 10 miles per hour
• The total weight on a scale if 5 pounds is placed there initially and a series of 10-pound weights are added
• The total wages earned by a waiter who is paid $5 per hour and earns $10 in tips
• The combined length of 5 boards, each 10 feet longer than the width of a doorway

Carlos is renovating a house and hires a plumber to install the piping for the new bathroom. The plumber charges an initial fee plus an hourly rate for the number of hours it will take to complete the installation. The function y=35x+100 can be used to model the total cost of the job, in dollars. What does the slope in the expression of this function represent?

• the initial fee for the installation, $35
• the initial fee for the installation, $100
• the cost per hour of installation work, $35
• the number of hours to complete the installation,