Modeling linear situations (ACT/SAT/PSAT 8/9/10). Game on.

Modeling linear situations (ACT/SAT/PSAT 8/9/10) 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 20 modeling linear situations (act/sat/psat 8/9/10) problems our math games drill.

CCSS 8.F.B.420 questions in the bank
Kickoff

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Warm-upeasy

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+30.y = 5x + 30\textsf{.}

Mid-gameeasy

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+12.y = 3x + 12\textsf{.}

Mid-gameeasy

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+75.y = 20x + 75\textsf{.}

Mid-gameeasy

A phone plan costs $25\text{\char36}25 per month plus $0.08\text{\char36}0.08 for each text message. Let xx be the number of texts and yy be the monthly bill in dollars. Which equation models the situation?

The monthly base cost is $25\text{\char36}25 (intercept) and each text adds $0.08\text{\char36}0.08 (slope), so y=0.08x+25.y = 0.08x + 25\textsf{.}

Mid-gameeasy

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+50.y = 8x + 50\textsf{.}

Mid-gameeasy

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=18x.y = 18x\textsf{.}

Mid-gameeasy

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=35x.y = 35x\textsf{.}

Buzzer beatereasy

A print shop already has 6464 posters ready for an event and prints an average of 3.53.5 more posters each hour. Let xx be the number of hours of printing and yy be the total number of posters ready. Which equation models the situation?

The shop starts with 6464 posters (intercept) and adds 3.53.5 posters each hour (slope), so y=3.5x+64.y = 3.5x + 64\textsf{.}

Overtime

12 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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Tests that cover modeling linear situations (act/sat/psat 8/9/10):
NAEPSBACPSAT 8/9SC READYNC EOG/EOC
Reporting domains for this skill
SAT All grades: AlgebraACT All grades: Preparing for Higher MathSTAAR Algebra I: Linear Functions, Equations, and InequalitiesSTAAR Grade 7: Computations and Algebraic RelationshipsSTAAR Grade 8: Computations and Algebraic RelationshipsMAP Growth Math 6+: Operations and Algebraic Thinking
More Grade 8 skills
Linear functions with an unknown constantMulti-step linear equationsSimilar triangle shadows (ACT/SAT/PSAT 8/9/10)Linear coefficient interpretations (SAT/PSAT 8/9/10)Rectangle diagonal from area (ACT)Triangle angle sumLinear Algebra Basics: SystemsPythagorean theorem in context (SAT/ACT)All Grade 8 practice →

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