SOLUTION: Consider the line . y=8x-8 Find the equation of the line that is perpendicular to this line and passes through the point .(2,4) Find the equation of the line that is parallel to th

Question 430682: Consider the line . y=8x-8 Find the equation of the line that is perpendicular to this line and passes through the point .(2,4) Find the equation of the line that is parallel to this line and passes through the point .(2,4)
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
y = 8x-8 is in slope-intercept form, y=mx+b.
slope = 8
y-intercept is where x=0, which is -8.
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A line perpendicular to a given line has a slope that is the inverse reciprocal.
Given the slope of the first line = 8, then a perpendicular line will have slope = -1/8.
,
We want this line to pass through (2,4). Its equation is:
y = -1/8x + b
.
Hmmm. We don't know b. (We can guess it would not be -8.)
.
But we can plug in the x & y we know (2,4) to determine what b has to be.
4 = -1/8(2) + b
4 = -1/4 + b
4 = -.25 + b
4.25 = b
So the equation of the perpendicular line is:
y = -1/8x + 4.25
.
I'm not sure what your last question about the parallel line references. Two parallel lines that go through the same point will lie on top of one another. Since a line has no third dimension, you cannot tell them apart.
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But we can find a line parallel to the original line that goes through (2,4).
y = 8x -8 is the original equation. But we don't care about the -8, because the intercept will shift to somewhere else for the parallel line.
y = 8x +b
4 = 8(2) +b
4 = 16 +b
-12 = b
So the equation of the parallel line is:
y = 8x -12
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We can check our answers with a graph.
.

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So the answers are:
A line perpendicular to the first line that passes through (2,4) is defined by the equation:
y = -1/8x + 4.25 (This is the green line.)
A line parallel to the first line that passes through (2,4) is defined by the equation:
y = 8x -12 (This is the blue line.)
.
Done.
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