--> -2y = -10 - x
--> y = 0.5x + 5

So the slope is 0.5 you got that right. Any line with that slope is parallel to y. So you start off with:
(I'll call the new line g to avoid confusion)

g = 0.5x

This is parallel to y.
Now the line has to go through (-1 ; 3), meaning when x is -1, y (g in this case) has to be -3, so plug that in:

-3 = 0.5 * (-1)

--> -3 = -0.5

Now you see that the equation isn't right. -3 isn't -0.5. To fix that, you subtract 2.5 from the right side:

- 3 = 0.5 * (-1) - 2.5

--> -3 = -0.5 - 2.5
--> -3 = -3

Now the equation is right. So the final thing in general form would be:

g = 0.5x - 2.5

or

y = 0.5x - 2.5 (if you like to use y)

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