SOLUTION: DIRECTIONS: Write the standard form of the equation through the point with the given slope. INFORMATION: (2,3), slope = undefined PROBLEM: I know I need to find the slope-

Question 325778: DIRECTIONS:
Write the standard form of the equation through the point with the given slope.
INFORMATION:
(2,3), slope = undefined
PROBLEM:
I know I need to find the slope-intercept form of the equation first, in order to find the standard form, but how do I do that if the slope is undefined? Please help. Thank you.
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 slope to be undefined, the denominator (the difference in the

-coordinates) has to be zero. In order for the denominator to be zero, the

-coordinates have to be equal. So a line with an undefined slope 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 2, 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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