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Question 1083363: Please explain how this is done, I want to be able to do this without help
Write an equation in slope-intercept form of the line satisfying the following conditions through (6,9); perpendicular to x=5
The equation of the line ______
(Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer.)
Found 3 solutions by Theo, rothauserc, natolino_2017:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! point is (6,9)
line is perpendicular to vertical line x = 5.
that means the line has to be horizontal.
that means the slope of the line is 0
that means the equation of the line is y = 9
the slope intercept form of the line would be y = 0*x + 9
0*x goes away and you are left with y = 9
here's a graph of both equations.
the intersection of the vertical line and the horizontal line is (5,9).
if the line y = 9 is perpendicular to the line x = 5, their sloped have to be negative reciprocals of each other.
the slope of the line y = 9 is equal to 0.
the slope of the line x = 5 is undefined.
a slope of 0 can have anything as the denominator because 0 divided by anything is equal to 0.
assuming the slope is 0/5, then the negative reciprocal would be -5/0 which is undefined.
how do you get an undefined slope?
the standard form of the equation of a straight line is ax + by = c
to convert to the slope intercept form, do the following:
start with ax + by = c
subtract ax from both sides of the equation to get by = c - ax
divide both sides of the equation by b to get y = c/b - ax/b
reorder the terms in descending order of degree to get y = -ax/b + c/b
if b = 0, then the slope is undefined because you can't divide anything by 0 and get a real answer.
therefore, the standard form of the equation has to be ax + 0y = c
simplify this to get ax = c
divide both sides by a to get x = c/a
c/a is a constant, therefore x = c
how does this work with x = 5?
start with ax + by = c
set b = 0 to get ax = c
solve for x to get x = c/a
since you know that x = 5, then c/a must be equal to 5.
this could happen in muiltiple ways.
one way is that c = 25 and a = 5.
you would then start 5x + by = 25
b is equal to 0 so you get 5x = 25
divide both sides by 5 and you get x = 5.
the general rule is:
a vertical line is shown as x = c
a horizontal line is y = c
c is any constant.
how do we get a horizontal line?
start with ax + by = c
convert to slope intercept form to get y = -ax/b + c/b
-ax/b is equal to 0 when a is equal to 0.
go back to standard form and replace a with 0 to get 0x + by = c
0x cancels out and you are left with by = c
solve for y to get y = c/b
it can be a little complicated to get through, but, if you remember that a horizontal line is perpendicular to a vertical line, then the solution is pretty clear.
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! We are given point (6, 9) and the line x = 5
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the line x = 5 intersects the x axis at the point (5, 0) and is perpendicular to the x axis, here is the graph of x = 5
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the definition of slope is (change in y) / (change in x)
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for our line x = 5, we see that every point on the line has an x value of 5 so our change in x is always 0 and division by 0 is indeterminate
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a line which is perpendicular to a given line has a slope equal to the negative reciprocal of the given line
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in our case that would be 0
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a line perpendicular to x = 5 is a line where the y coordinate is fixed
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in order for the line to go through the point (6, 9), we have y = 9
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again looking at our definition of slope the difference in y coordinates is 0(9-9) and x value differences are not = to zero, therefore the slope is 0
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here is a graph of y = 9 along with x = 5
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Answer by natolino_2017(77)  (Show Source):
You can put this solution on YOUR website! First of all, the line x=5 is a vertical line.
So any perpendicular line to x=5 would be horizontal.
If the line is horizontal the slope is zero.
so the line woul be y = b.
which means that for any value of x, the y = b.
if the (6,9) must be in the line, then b = 9.
So the answer is y = 9
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