The equation of the perpendicular line is y = -2x + 4
How to determine the line equation?
The line equation is given as:
2x = 4y - 8
Make y the subject
4y = 2x +8
Divide by 4
y = 0.5x + 2
The slope of the above equation is
m = 0.5
The slopes of perpendicular lines are opposite reciprocals.
This means that, the slope of the perpendicular line is:
n = -1/m
This gives
n = -1/0.5
n = -2
The equation is then calculated as:
y = n(x - x1) + y1
This gives
y = -2(x - 1) + 2
Expand
y = -2x + 2 + 2
Evaluate
y = -2x + 4
Hence, the equation of the perpendicular line is y = -2x + 4
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