Because the xx value for both points are the same, -2−2, we know the line going through these two points is a vertical line with the equation:
x = -2x=−2
For each and every value of yy, xx is equal to -2−2.
By definition, the slope of a vertical line is undefined.
We can show this as follows:
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))m=y2−y1x2−x1
Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) are the two points on the line.
Substituting the values from the points in the problem gives:
m = (color(red)(4) - color(blue)(-2))/(color(red)(-2) - color(blue)(-2)) = (color(red)(4) + color(blue)(2))/(color(red)(-2) + color(blue)(2)) =6/0m=4−−2−2−−2=4+2−2+2=60
We can not divide by 00 therefore the slope is undefined.
