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2. The graph shows one rectangle whose perimeter is 50 units, and has its lower left vertex at the origin and two sides on the axes. On the same graph, draw more rectangles with perimeter 50 units using the values from your table. Make sure that each rectangle has a lower left vertex at the origin and two sides on the axes.

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Learning Targets

In this lesson, students extend their previous work to include equations for horizontal and vertical lines.
The goal of this lesson and the next is to start getting students to think about linear equations in two variables in a different way in preparation for their work on systems of linear equations in the next unit.

I can write equations of lines that have a positive or a negative slope.
I can write equations of vertical and horizontal lines.
I know that the graph of an equation is a visual representation of all the solutions to the equation.
I understand what the solution to an equation in two variables is.

Success Criteria

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10.2 apples & oranges

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?

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Are you Ready for more?

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?

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10.3 solutions and everything else

You have two numbers. If you double the first number and add it to the second number, the sum is 10.

Let x represent the first number and let y represent the second number. Write an equation showing the relationship between x, y, and 10.

Draw and label a set of x- and y-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?

List ten points that do not 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?

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Lesson Summary

Horizontal lines in the coordinate plane represent situations where the y value doesn’t change at all while the x value changes. For example, the horizontal line that goes through the point (0, 13) can be described in words as “for all points on the line, the y value is always 13.” An equation that says the same thing is y = 13.

Vertical lines represent situations where the x value doesn’t change at all while the y value changes. The equation x = -4 describes a vertical line through the point (-4, 0).

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Lesson Summary

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Lesson Summary

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10.4 Cool Down: identify the points

Which of the following coordinate pairs make the equation x - 9y = 12 true?

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Reflections

• Can you write equations of lines that have a positive or a negative slope?

• Can you write equations of vertical and horizontal lines?

• Do you know that the graph of an equation is a visual representation of all the solutions to the equation?

• Do you understand what the solution to an equation in two variables is?

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