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Answer on Algebra Question for Kurt
Question #5949
Write an equation in standard form for the line perpendicular to y=1/2x+2 and passes through (6,3).
Expert's answer
Answer
Let's write the given equation in a formx/2 + y = 2.
We see that the the direction vector of this line is
(1/2, 1).
Let's seek the perpendicular line in a form
ax + by = c.
It's direction vector is (a,b). As these two lines are perpendicular, we have that
(1/2, 1)*(a,b) =& a/2 + b = 0 ==> b = a/2
We obtain
ax  ay/2 = c.
Let substitute point (6, 3):
6a&  a(3)/2 = c
a:=1 ==> b = 1/2
Now,
6 + 3/2 = c
and
c = 7.5,
so
x&  y/2 = 15/2
and at last
2x  y = 15.
We have the equation of the line in standard form:
y = 2x  15.
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