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X + y less than or equal to 2

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Answer:

Explanation:

Symbolically written, we have:

x + y ≤ 2

We can graph this to determine where the solution points lie:

Temporarily write this as x + y = 2. Find the x- and y-intercepts:

Letting x = 0 yields y = 2: (0, 2)

Letting y = 0 yields x = 2: (2, 0)

Plot these two points. Draw a line through them. You'll see that this line has a negative slope: m = -2.

Now determine whether you should shade the area above this line or below it. Arbitrarily choose test point (-3, 1) and substitute -3 for x and 1 for y in x + y ≤ 2: -3 + 1 ≤ 2, or -2 ≤ 2. This is true. This test point is BELOW the line, so it's on the "right" side of the line; thus you should shade the graph below this line.

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