The equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4
How to determine the equation of a line perpendicular?
The equation is given as:
2x + 2y = - 10
The point it passes through is given as (6, 2) .
Recall that
2x + 2y = - 10
Divide through by 2
x + y = -5
Make y the subject
y = -x - 5
The slope of the above equation is
m = -1
The slopes of perpendicular lines are opposite reciprocals.
So, we have
m2 = -1/-1
Evaluate
m2 = 1
Recall that the point it passes through is given as (6, 2) .
So, the equation is represented as:
y = m2(x - x1) + y1
This gives
y = 1(x - 6) + 2
Open the bracket
y = x - 6 + 2
Evaluate
y = x - 4
Hence, the equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4
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