HELP 80 POINTS DUE SOON

Answer:

a = 1

Step-by-step explanation:

The important point here is that both lines are horizontal reflections of each other. If we treat the line x = a as a kind of "mirror" for these lines, every point at the same y value on each line is going to be an equal horizontal distance from that "mirror". If that's confusing, think about how, as you pull your hand away from a mirror, your hand's reflection seems to go deeper into it. As you bring it closer, your reflection gets closer too. And when you're touching the mirror, it seems like your hand and its reflection are touching!

We want to find that "touching" point for the two lines, the intersection, because it'll tell us exactly where our "mirror" - more commonly called the axis of symmetry - is. The point of intersection of any two lines is the point where their equations are exactly equal to each other.

Our equations are y = 3x - 5 and y = 1 - 3x, so setting those two equal to each other and solving for x:

[tex]3x-5=1-3x\\6x=6\\x=1[/tex]

This tells us that the two lines intersect at x = 1, which is exactly our axis of symmetry, so a = 1!

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