Question 674316: A line that passes midway between and is parallel to both x - y = 6 and x - y = -6.
Answer by jokaehler(26)   (Show Source):
You can put this solution on YOUR website! In order to figure out where these are, we need to find the y-intercepts of the given equations, and find halfway between the two.
Let's start with x - y = 6.
Add "y" to both sides
x = y + 6
Subtract "6" from both sides so that we end up with...
x - 6 = y
Rearrange it in y = mx + b form...
y = x - 6
The y-intercept is (0, -6).
Now for x - y = -6.
Add "y" to both sides
x = y - 6
Add "6" to both sides
x + 6 = y
Rearrange...
y = x + 6
the y-intercept is (0,6)
Since the two intercepts are (0, -6) and (0, 6), we need to find the midpoint between the two y-intercepts. Since they are both six apart from the origin, the center point between the two lines is "0." In order to run parallel, we need the slope to be the same with the y-intercept at 0.
y = 1x + 0
Which simplifies to...
y = x
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