One way to identify the relative position of 2 lines is to compare their slopes.
For instance, if 2 lines are parallel, their slopes must be equal. Or, if 2 lines are perpendicular, the product of their slopes is -1.
The slope could be identified, writing the equation in the standard form:
y = mx + n, where m is the slope and n is the y intercept.
We'll put each given equation in the standard form. We'll start with the first one.
We'll isolate y to the left side:
y = -2x + 23
m1 = -2
The 2nd equation is written in the standard form, already:
m2 = -2
Since the slopes m1 = m2 = -2, the lines are parallel.
We recast both equations in the slope intercept form of y = mx+c and then see whether both lines represented by the equations have the same slope m to be parallel.
The first given equation y + 2x = 23 . We reacast it as : y = -2x +23....(1)
The other equation y = -2x+11...(1) is in the slope intercept form itself.
Both equations of lines have the same slope of -2. So they are inclined at the same angle to the x axis. So both of the equations represent parallel lines.