HELP 80 POINTS DUE SOON
2 answers:
Answer:
a = 1
Step-by-step explanation:
The important point here is that both lines are <em>horizontal reflections</em> 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 <em>intersection</em>, because it'll tell us exactly where our "mirror" - more commonly called the <em>axis of symmetry</em> - 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:
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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For this case we have that by definition, the point-slope equation of a line is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have two points:
We found the slope:
Thus, the equation is of the form:
We substitute one of the points and find "b":
Finally, the equation is:
Answer: