Question 326105: Write the equation for the following problem? a vertical line that passes through (4,-7)
Found 2 solutions by vksarvepalli, solver91311:
Answer by vksarvepalli(154)   (Show Source):
You can put this solution on YOUR website! vertical line means a line that is parallel to the y axis
a line parallel to the y axis will be of the form x= some constant
now here the line is passing through the point (4,-7)
so the equation of the line is x=4.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Recall the slope formula: The difference in the  -coordinates divided by the difference in the  -coordinates.
In order for the line to be vertical, -coordinates have to be equal. If the -coordinates are equal, the denominator (the difference in the -coordinates) has to be zero. If the denominator is zero, the slope is undefined. So a vertical line has an undefined slope and is a set of ordered pairs where all of the -coordinates are identical. If you want your vertical line to pass through the point ) , then all of the points on your line must have an -coordinate of 4, and you don't care what the -coordinate value is. The only way to describe such a set of ordered pairs is:
Which, if you consider the possibility of writing it as:
is, as you can see, written in Standard Form. The equation of a vertical line is the only equation of a line that CANNOT be written in slope-intercept, point-slope, or two-point form because all of these forms require expressing the slope.
John
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