Slope-Intercept Form Applications - Guided Problems (p21-23)

#2) Mark bought a season ticket to the ski resort for $395, however, he must pay $25 to rent skis each time he goes skiing.

Define the variables.

• x = # of visits

  y = total cost

• x = cost to ski each time

  y = total cost

• x = total cost

  y = # of visits

Answer explanation

Independent Variable: x = # of visits

Dependent Variable: y=total cost

#2) Mark bought a season ticket to the ski resort for $395, however, he must pay $25 to rent skis each time he goes skiing.

Identify the rate of change and the initial value.

• Rate: $25/visit

  Initial Value: $395

• Rate: $395/visit

  Initial Value: $25

Answer explanation

Rate of Change m= $25/visit

Initial Value b = $395

Tags

CCSS.HSF.LE.B.5

#2) Mark bought a season ticket to the ski resort for $395, however, he must pay $25 to rent skis each time he goes skiing.

Which equation models the problem?

Answer explanation

Equation: y=25x+395

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

#3) Jane bought a car with 23,000 miles on it.  She determined that she typically drives 12,000 miles per year.

Define the variables.

• x = total miles

  y = # of years

• x = # of years

  y = total miles

• x = 11000

  y = total miles

Answer explanation

Independent Variable: x = # of years

Dependent Variable: y = total miles

Tags

CCSS.6.EE.C.9

#3) Jane bought a car with 23,000 miles on it.  She determined that she typically drives 12,000 miles per year.

Which value represents a rate?

Type the number only.

Mathematical Equivalence

OFF

Answer explanation

RATE OF CHANGE m = $12,000 miles/yr

Tags

CCSS.7.EE.B.4A

#3) Jane bought a car with 23,000 miles on it.  She determined that she typically drives 12,000 miles per year.

What is the initial value (starting amount)?

Type the number only.

Mathematical Equivalence

OFF

Answer explanation

INITIAL VALUE b = 23,000 miles

Tags

CCSS.HSF.LE.B.5

#3) Jane bought a car with 23,000 miles on it.  She determined that she typically drives 12,000 miles per year. 

Which equation models the problem?

Answer explanation

Equation: y=12000x+23000

Tags

CCSS.6.EE.C.9

#3) Jane bought a car with 23,000 miles on it.  She determined that she typically drives 12,000 miles per year.

How would you use the equation to determine how many years it might take for the odometer to read 99,999?

• Replace y with 99999 and solve for x.

• Replace x with 99999 and solve for y.

• Multiply 11000 by 99999

Answer explanation

Since y represents the # of miles on the odometer and x represents the # of years , replace y with 99999 and solve for x.

#4) There are 18 gallons of gas in a car at the beginning of a road trip.  Each hour into the trip, 2.5 gallons of gas are used. 

Define the variables.

• x = # of gallons of gas remaining

  y = # of hours

• x = # of hours

  y = # of gallons of gas remaining

• x = 2.5

  y = 18

Answer explanation

x = # of hours

y = # of gallons of gas remaining

( Be sure to write the variable definitions on your paper)

Tags

CCSS.6.EE.C.9

#4) There are 18 gallons of gas in a car at the beginning of a road trip.  Each hour into the trip, 2.5 gallons of gas are used. 

Which value represents a rate?

Mathematical Equivalence

OFF

Answer explanation

Gas is being used at a rate of of 2.5 gallons per hour. The rate of change is negative.

RATE OF CHANGE m = -2.5 gal/hr

Tags

CCSS.HSF-LE.A.1B