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

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#