… my question is … Don't I have to find x and then use that to find y?
That's possible, in
some exercises, but we'd need more information before we could find a particular number for x. Without more information, x could be any Real number. Here are some example (x,y) pairs that satisfy the equation y=2x-6.
(3, 0) \(\;\) (22003, 44000) \(\;\) (5/2, -1) \(\;\) (3.9, 1.8)
I don't know whether you've learned about graphing points, but those types of exercises might ask us to find y for some values of x, and we get to pick the numbers. We calculate the y-value for each x we choose. Let's choose x=3. In the equation, we replace symbol x with the number 3 and write:
y = 2(3) - 6
After substituting 3 for symbol x, we do the arithmetic (using the Order of Operations).
y = 6 - 6
y = 0
The (x, y) pair is (3, 0) and it's just one solution for the equation. If we calculate many (x,y) pairs and draw the points, they form a straight line.
In other exercises, we might need to pick a number for y first, and then find x. Or maybe we're given a specific number for y (like 44000) and we then solve 44000=2x-6 for x. There are many different things we can do with the equation y=2x-6.
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