IM 8.3.12 Lesson: Solutions to Linear Equations

Which figure has the largest shaded region?
[img]data:image/png;base64,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[/img]
Explain how you know.
At the corner produce market, apples cost $1 each and oranges cost $2 each. Find the cost of:
6 apples and 3 oranges
4 apples and 4 oranges
5 apples and 4 oranges
8 apples and 2 oranges
Noah has $10 to spend at the produce market. Can he buy 7 apples and 2 oranges?
Explain or show your reasoning.
What combinations of apples and oranges can Noah buy if he spends all of his $10?
Use two variables to write an equation that represents $10-combinations of apples and oranges. Be sure to say what each variable means.
What are 3 combinations of apples and oranges that make your equation true? What are three combinations of apples and oranges that make it false?
Graph the equation you wrote relating the number of apples and the number of oranges.
What is the slope of the graph?
What is the meaning of the slope in terms of the context?
Suppose Noah has $20 to spend. Graph the equation describing this situation.
What do you notice about the relationship between this graph and the earlier one?
You have two numbers. If you double the first number and add it to the second number, the sum is 10.
Let [math]x[/math] represent the first number and let [math]y[/math] represent the second number.  Write an equation showing the relationship between [math]x[/math], [math]y[/math], and 10.
Draw and label a set of [math]x[/math]- and [math]y[/math]-axes. Plot at least five points on this coordinate plane that make the statement and your equation true. What do you notice about the points you have plotted?[br]
List ten points that do [i]not[/i] make the statement true. Using a different color, plot each point in the same coordinate plane. What do you notice about these points compared to your first set of points?[br]

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