When writing an equation in point-slope format, is it not proper to fully solve for y?

Question

For example, here is my problem:
Find the point-slope equation for a line containing the point (-7, 2) and the slope m = 3.
The answer was this:
y – 2 = 3(x + 7)
I was under the impression that you would solve for y by adding two to both sides, distributing the 3, etc, but a lot of answers I am seeing are showing like this. What is correct?

Thank you.

Answer 1

The equation y – 2 = 3(x + 7)
is considered point-slope form, since you can "see" the point and the slope.

solving for y, ...
y-2= 3x+21
y = 3x + 23 , gives you what is called the slope-yintercept form, because you can blatantly "see" the slope and the y-intercept

If you arrange it so that everything is on the left side, writing the x term first as a positive term, it is called the general form :
y - 2 = 3x + 21
-3x + y - 23 = 0
3x - y + 23 = 0

some texts and authors consider 3x - y = -23 to be "standard form"

Answer 2

What if both of your points were negative, such as (-7, -3), slope of 3
Would you write it as y - (-3) = 3(x - (-7)
and leave it like that, or would the correct answer in point-slope form be
y + 3 = 3(x + 7)

Thank you