Grade 8 · Algebra & functions

Modeling linear situations practice

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.

CCSS 8.F.B.410 questions in the bank
Sample questions

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Question 1easy

A taxi charges a $4\text{\char36}4 boarding fee plus $2.50\text{\char36}2.50 for each mile driven. Let xx be the number of miles and yy be the total cost in dollars. Which equation models the situation?

The per-mile rate is the slope ($2.50\text{\char36}2.50) and the flat boarding fee is the yy-intercept ($4\text{\char36}4), so y=2.5x+4y = 2.5x + 4.

Question 2easy

A gym charges a $30\text{\char36}30 monthly membership plus $5\text{\char36}5 for each fitness class. Let xx be the number of classes and yy be the total monthly cost in dollars. Which equation models the situation?

Each class adds $5\text{\char36}5 (slope) on top of the $30\text{\char36}30 membership (intercept), so y=5x+30y = 5x + 30.

Question 3easy

An amusement park charges $12\text{\char36}12 for admission and $3\text{\char36}3 for each ride. Let xx be the number of rides and yy be the total cost in dollars. Which equation models the situation?

Admission is the starting cost ($12\text{\char36}12) and each ride adds $3\text{\char36}3, so y=3x+12y = 3x + 12.

Question 4easy

Elena already has $75\text{\char36}75 in her savings account and deposits $20\text{\char36}20 each week. Let xx be the number of weeks and yy be the account balance in dollars. Which equation models the situation?

She starts at $75\text{\char36}75 (intercept) and gains $20\text{\char36}20 per week (slope), so y=20x+75y = 20x + 75.

Question 5easy

A school club starts a fundraiser with $50\text{\char36}50 already collected and earns $8\text{\char36}8 for each cake sold. Let xx be the number of cakes sold and yy be the total money raised in dollars. Which equation models the situation?

The club begins at $50\text{\char36}50 and gains $8\text{\char36}8 per cake, so y=8x+50y = 8x + 50.

Question 6easy

A kayak rental shop charges $18\text{\char36}18 per hour with no upfront fee. Let xx be the number of hours rented and yy be the total cost in dollars. Which equation models the situation?

With no starting fee, the cost is only the hourly rate times hours: y=18xy = 18x.

Question 7easy

A tutor charges $35\text{\char36}35 per session and no registration fee. Let xx be the number of sessions and yy be the total cost in dollars. Which equation models the situation?

Each session costs $35\text{\char36}35 with no upfront charge, so y=35xy = 35x.

Question 8medium

The temperature outside is 68F68^\circ\text{F} at sunset and drops 2F2^\circ\text{F} each hour. Let xx be the number of hours after sunset and yy be the temperature in degrees Fahrenheit. Which equation models the situation?

The temperature starts at 6868 and falls 22 degrees per hour, so y=2x+68y = -2x + 68.

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