options: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
problem_activity: When Janaya started working, she researched how income tax was determined. She read that income up to and including $10,000 is taxed at a rate of 10%. Any income over $10,000 and up to and including $40,000 is taxed at a rate of 15%. For example, if Janaya earned $11,000 in one year, the first $10,000 would be taxed at a rate of 10% and the last $1,000 would be taxed at a rate of 15%.
How much income tax would Janaya pay if she earned $15,000 in one year?
Write a piecewise function to represent the situation.
How much more income tax would a person who earns $30,000 pay than a person who earns $10,000 in one year?


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