SOLUTION: A line passing through (2, -4) and (-4, y) is perpendicular to a line with slope 3/2. What is the value of y?

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Question 178465: A line passing through (2, -4) and (-4, y) is perpendicular to a line with slope 3/2. What is the value of y?
Answer by josmiceli(9686) About Me  (Show Source):
You can put this solution on YOUR website!
Given 1 point and the slope of a line I can
find the equation of that line
(2,-4) is a point on the line
If m is the slope, -%281%2Fm%29 is
perpendicular to the line with that slope
-%281%2F%283%2F2%29%29+=+-%282%2F3%29
The general slope-intersect form of a line is
y+=+mx+%2B+b
So far I have
y+=+-%282%2F3%29x+%2B+b
To determine b I use the given point
-4+=+-%282%2F3%29%2A2+%2B+b
-4+=+-%284%2F3%29+%2B+b
-12+=+-4+%2B+3b
3b+=+-8
b+=+-%288%2F3%29
The equation of the line is
y+=+-%282%2F3%29x+-%288%2F3%29
To find the y in (-4,y),
y+=+-%282%2F3%29%2A%28-4%29+-+%288%2F3%29
y+=+8%2F3+-+%288%2F3%29
y+=+0 answer