A taxi charges a boarding fee plus for each mile driven. Let be the number of miles and be the total cost in dollars. Which equation models the situation?
The per-mile rate is the slope () and the flat boarding fee is the -intercept (), so .
Modeling linear situations is a grade 8 math skill aligned to Common Core standard 8.F.B.4: construct a function to model a linear relationship between two quantities; determine the rate of change and initial value of the function. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 modeling linear situations problems our math games drill.
A taxi charges a boarding fee plus for each mile driven. Let be the number of miles and be the total cost in dollars. Which equation models the situation?
The per-mile rate is the slope () and the flat boarding fee is the -intercept (), so .
A gym charges a monthly membership plus for each fitness class. Let be the number of classes and be the total monthly cost in dollars. Which equation models the situation?
Each class adds (slope) on top of the membership (intercept), so .
An amusement park charges for admission and for each ride. Let be the number of rides and be the total cost in dollars. Which equation models the situation?
Admission is the starting cost () and each ride adds , so .
Elena already has in her savings account and deposits each week. Let be the number of weeks and be the account balance in dollars. Which equation models the situation?
She starts at (intercept) and gains per week (slope), so .
A school club starts a fundraiser with already collected and earns for each cake sold. Let be the number of cakes sold and be the total money raised in dollars. Which equation models the situation?
The club begins at and gains per cake, so .
A kayak rental shop charges per hour with no upfront fee. Let be the number of hours rented and be the total cost in dollars. Which equation models the situation?
With no starting fee, the cost is only the hourly rate times hours: .
A tutor charges per session and no registration fee. Let be the number of sessions and be the total cost in dollars. Which equation models the situation?
Each session costs with no upfront charge, so .
The temperature outside is at sunset and drops each hour. Let be the number of hours after sunset and be the temperature in degrees Fahrenheit. Which equation models the situation?
The temperature starts at and falls degrees per hour, so .
Questions like these are served inside our head-to-head math games.
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