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You surely mean whether the lines represented by the equations are parallel, perpendicular or neither.
To test this, we have to keep in mind that the slope of parallel lines is the same and the product of the slope of perpendicular lines is -1.
Here the equation of the lines are in the form y = mx + c, where m is the slope
y = 23 - 2x , slope = -2
y = -2x +11, slope = -2
As the slope of the lines is equal they are parallel.
The relative position of 2 lines is established when comparing 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.
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