M.A1HS.46
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Example Problems
A survey recorded car ownership across different regions.
What fraction of rural respondents own an SUV?
| Car Type | Urban | Rural | TOTAL |
|---|---|---|---|
| Sedan | 50 | 30 | 80 |
| SUV | 40 | 50 | 90 |
| Truck | 10 | 20 | 30 |
| TOTAL | 100 | 100 | 200 |
What fraction of rural respondents own an SUV?
Researchers surveyed public support for renewable energy.
What fraction of conservatives oppose renewable energy?
| Ideology | Support | Oppose | TOTAL |
|---|---|---|---|
| Liberal | 70 | 10 | 80 |
| Conservative | 50 | 30 | 80 |
| Moderate | 40 | 20 | 60 |
| TOTAL | 160 | 60 | 220 |
What fraction of conservatives oppose renewable energy?
A nutritional survey measured daily fruit intake.
What fraction of the total sample eat 3 or more servings daily?
| Intake | Male | Female | TOTAL |
|---|---|---|---|
| 0 servings | 20 | 15 | 35 |
| 1–2 servings | 50 | 60 | 110 |
| 3+ servings | 30 | 25 | 55 |
| TOTAL | 100 | 100 | 200 |
What fraction of the total sample eat 3 or more servings daily?
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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