To clarify, it seems you might be dealing with a pair of linear equations that represent two lines. You specified "y = x + 3" and "y = x - 3".
Let's analyze these equations:
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The first equation, \( y = x + 3 \), is a line with a slope of 1 and a y-intercept of 3. This means it rises one unit in the y-direction for every one unit it moves in the x-direction.
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The second equation, \( y = x - 3 \), is also a line with the same slope of 1 but a y-intercept of -3.
When graphing these two lines, \( y = x + 3\) will be the upper function because it lies above \( y = x - 3 \) for all values of \( x \).
If you are looking to create an absolute value equation from these lines, you might think of the upper function as the main equation, and the lower function as the negation of the distance from the x-axis. The absolute value represents the distance from the x-axis.
To express the region between these two lines using absolute value, we could write the function as follows:
\[ y = |x - 3| + 3 \]
This formulation reflects the two corners at \( (3,0) \) and \( (-3,0) \), while the lines themselves represent the different cases of the absolute value function.