Amanda's sewing a flag for a competition. The dimensions of her flag are shown below. Approximately, how many square yards of black material will Amanda need to make the flag?

To calculate the area of the black material on the flag, we need the shape and the dimensions of the black material itself.

Since the question is incomplete, as the dimension of the flag and the dimension of the black material are not given, I will provide a general explanation

Assume the shape of the black material is a rectangle.

The area will be calculated as:

Take for instance;

The area is:

Assume the shape of the black material is a square.

The area will be calculated as:

Take for instance;

The area is:

Assume the shape of the black material is a triangle

The area will be calculated as:

Take for instance;

The area is:

So, in general.

You need to first get the shape of the black segment on the flag, then calculate the area using the appropriate formula.

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All you have to do is plug in the x and y values for each ordered pair into the left hand side of the equation and see if you get 15 = 15. If you do, the ordered pair is a solution; otherwise it is not a solution. For example, let's try (-2,-3); that is x = -2 and y = -3:

2x - 9y = 15
2(-2) - 9(-3) = 15
-4 - (-27) = 15
-4 + 27 = 15
23 = 15

This is obviously not true, so (-2,-3) is not a solution. Now you try it on each of the ordered pairs given in the problem statement.