Question 419348: I need to accurately graph the absolute equation of
|x| + |y| = 2. I constructed a plot chart; first column the abs x, the second column the y coordinate to equal 2.
-3 - -
-2 0 2
-1 -1/1 2
0 -2/2 2
1 -1/1 2
2 0 2
3 - -
The graph that I came up with is a diamond shape with the x-intercepts of -2 and 2 and the y-intercepts of -2 and 2. Have I figured the problem correctly.
Found 2 solutions by duckness73, stanbon:
Answer by duckness73(47)   (Show Source):
You can put this solution on YOUR website! Your answer is correct, but I'm sure that you want a more rigorous answer than a plot graph. Here's how you do it. Look at each quadrant separately. In the first quadrant, x and y are both positive, so the absolute values just equal the variables, x + y = 2. So, you graph this line but keep ONLY IN THE PART IN THE FIRST QUADRANT. This will give you your upper right side of your diamond. Then look in the second quadrant. In the second quadrant, x is negative and y is positive. For x, the absolute value of x when x is negative is -x ... in other words |x| = -x for x in the second quadrant. So graph the equation -x + y = 2 but only keep the part of the graph IN THE SECOND QUADRANT. This is your upper left side of the diamond. In the third quadrant, x and y are both negative, so using similar reasoning as the previous case, graph the line -x - y = 2 but keep ONLY THE THIRD QUADRANT. This is your lower left side of the diamond. In the fourth quadrant, where x is positive and y is negative, graph x - y = 2 but keep ONLY THE FOURTH QUADRANT. This is the lower right side of your diamond. You have now considered all four cases and kept only the portions of the graphs for the appropriate quadrants.
Answer by stanbon(75887)  (Show Source):
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