13y-x=7 and 7-y/2=x are parallel, neither or perpendicular lines
since the slopes are not the same, not parallel
since the slopes are not negative reciprocals, not perpendicular
To determine whether the two lines are parallel, perpendicular, or neither, we will compare their slopes.
First, let's rearrange both equations into the slope-intercept form (y = mx + b), where m represents the slope:
Equation 1: 13y - x = 7
Rearranging, we get: 13y = x + 7
Dividing by 13: y = (1/13)x + 7/13
Equation 2: 7 - y/2 = x
Rearranging, we get: y/2 = -x + 7
Multiplying by 2: y = -2x + 14
Now we can compare the slopes:
The slope of Equation 1 is (1/13), and the slope of Equation 2 is -2.
Since the slopes are not equal, the lines are not parallel.
To determine if they are perpendicular, we can multiply the slopes. If the product is -1, then the lines are perpendicular.
(1/13) * (-2) = -2/13
Since the product is not -1, the lines are not perpendicular either.
Therefore, the given equations represent neither parallel nor perpendicular lines.