why the equation of a vertical line cannot be in slope intercept form
2006-12-06 12:38:41 · 7 answers · asked by Anonymous in Education & Reference ➔ Homework Help
because that line only uses x and for the slope intercept form you use both y and x.
2006-12-06 12:42:03 · answer #1 · answered by refreshed 2 · 1⤊ 0⤋
This is true because there is no defined slope of a vertical line. In other words, there is no possible value for 'm' in the equation y=mx+b.
To prove that there is no slope for a vertical line, get the slope of any two points on the line. Using the line x = 5 as an example, choose two random points and get the slope of the line between them.
I'll use (5, 7) and (5, 1).
The slope would be (7-1) / (5-5)
This comes out to be 6 / 0
This is undefined since zero can never be the denominator of any fraction.
In other words, since any two points on a vertical line have the same x value, the denomiator of the slope would come out to be 0, and 0 cannot be in the denominator of a fraction.
Since there is an undefined slope, there is no value for 'm' in y = mx + b
2006-12-06 20:53:55 · answer #2 · answered by mike m 2 · 1⤊ 0⤋
because the slope of a vertical line is undefined. to show you how it is undefined take the rise over the run
if you take the rise of a vertical line, you have infinity/0, which is undefined. if you try writing that in y=mx+b...you get
y=(infinity/0)x+b.
y-b=(infinity/0)x....multiply both sides by zero
0=(infinity)x...which obviously doesn't make sense if you plug in any number other than 0 into x.
so if you take a previous form of the equation (i'm making this up as I go) say... the (y-b)X0=infinity(x) and plug in a number for y, then your x will not be effected by the y because it will always equal zero. This is why it is undefined, because it never makes sense when you actually try plugging in a y.
So, the equation is just written as x=c...or some number like x=6, because if it is in slope intercept form, you will have an undefined number in front of x. Does that make sense?
2006-12-06 20:55:02 · answer #3 · answered by Anonymous · 0⤊ 0⤋
The slope of a vertical line is not defined. Slope is defined as "rise over run", and since there is no "run" (change in the X direction), the slope is irrelevant.
2006-12-06 20:48:07 · answer #4 · answered by scottr9 3 · 0⤊ 0⤋
A vertical line has no slope
2006-12-06 20:47:39 · answer #5 · answered by lisa42088 3 · 1⤊ 0⤋
Because the slope is undefined.
And the equation has to be x=.
2006-12-06 21:10:40 · answer #6 · answered by Jo 2 · 0⤊ 0⤋
the equation of a verical line has to be a number equal to x.
ex: x=6
it is therefore impossible for it to be written in a y=mx+b format.
2006-12-06 20:42:48 · answer #7 · answered by ? 2 · 0⤊ 0⤋