Question

How do you write the equation of a line in slope intercept, point slope and standard form given (2,2) and (2,-3)?

Answer 1

See a solution process below:

Explanation:

First, we can determine the slope of the line:

The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(-3) - color(blue)(2))/(color(red)(2) - color(blue)(2)) = -5/0`

Because we cannot divide by `0` the slope of the line is undefined. Vertical lines by definition have an undefined slope.

Vertical lines have the property of for each and every value of `y` the `x` value is the same. In this problem `x` is equal to `2` for both points. Therefore, the equation of this line is:

`x = 2`