Question 1083363
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.