You should convert the two equations to slope intercept form, `y = mx+b` , and then you may compare the slopes m of the lines. If the slopes of lines have equal values, then the lines are parallel.

You need to convert the given form of equation `x+y=2`  to slope intercept form, hence, you need to keep y to the left side and you should move x to the right such that:

`y = -x + 2`

You need to convert the given form of equation `3x=8-3y`  to slope intercept form, hence, you need to move `-3y ` to the left side and you should move `3x`  to the right such that:

`3y = -3x + 8`

You need to divide by 3 such that:

`y = -x + 8/3`

Comparing the slopes of the lines (coefficients of x) you may notice that they have the same value -1.

Hence, using the slopes of the lines, you may conclude, without graphing, that the given lines are parallel.