FA.ACE.2
Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.)
Example Problems
A costume shop designs hats and wigs.
Let represent the number of hats and represent the number of wigs the shop can produce with its daily supply of fabric: .
The shop wants to design 3000 hats daily. How many wigs at most can the shop produce daily with the remaining supply of fabric?
Let represent the number of hats and represent the number of wigs the shop can produce with its daily supply of fabric: .
The shop wants to design 3000 hats daily. How many wigs at most can the shop produce daily with the remaining supply of fabric?
A publishing company prints newspapers and magazines.
Let x represent the number of newspapers and m represent the number of magazines the company can print with its daily supply of ink cartridges: .
The company wants to print 8000 newspapers daily. How many magazines at most can the company print daily with the remaining number of ink cartridges?
Let x represent the number of newspapers and m represent the number of magazines the company can print with its daily supply of ink cartridges: .
The company wants to print 8000 newspapers daily. How many magazines at most can the company print daily with the remaining number of ink cartridges?
A cafe serves lattes and fruit smoothies.
Let represent the number of lattes and represent the number of smoothies the cafe can make with its daily supply of milk: .
The cafe plans to make 2,000 lattes each day. How many smoothies at most can the cafe make each day with the remaining supply of milk?
Let represent the number of lattes and represent the number of smoothies the cafe can make with its daily supply of milk: .
The cafe plans to make 2,000 lattes each day. How many smoothies at most can the cafe make each day with the remaining supply of milk?
Khan Academy ResourcesSlope-intercept form reviewAge word problemsWriting linear equations word problemsSystems of equations word problemsSlope from graphLinear models word problemsModeling with multiple variablesGraphing linear relationships word problemsSlope-intercept equation from graphGraph labels and scalesModeling with sinusoidal functions: phase shiftConstruct exponential modelsModeling with sinusoidal functionsSystems of equations with elimination: x-4y=-18 & -x+3y=11Systems of equations with elimination: King's cupcakesSystems of equations with elimination: potato chipsSystems of equations number of solutions: fruit prices (1 of 2)Systems of equations number of solutions: fruit prices (2 of 2)Age word problem: Ben & WilliamAge word problem: Arman & DiyaAge word problem: ImranSlope-intercept equation from graphSlope-intercept form problemsSystems of equations with elimination: TV & DVDRational equations word problem: combined rates (example 2)Rational equations word problem: eliminating solutionsSlope-intercept equation from slope & pointSlope-intercept equation from two pointsSolutions to systems of equations: consistent vs. inconsistentSystems of equations with substitution: coinsRational equations word problem: combined ratesConstructing exponential models: percent changeTrig word problem: modeling annual temperatureTrig word problem: length of day (phase shift)Modeling with multiple variables: Roller coasterConstructing exponential models: half lifeLinear functions word problem: icebergLinear functions word problem: paintModeling with multiple variables: PancakesLinear functions word problem: poolSystems of equations with elimination: coffee and croissantsConstructing linear equations from contextSystem of equations word problem: infinite solutionsSystems of equations with elimination: apples and orangesSystem of equations word problem: no solutionSystem of equations word problem: walk & rideConstructing exponential modelsTrig word problem: modeling daily temperatureModeling with basic exponential functions word problem
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