How do you find the slope given (-2,-2) and (-2,4)?

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Answer 1 · 2017-08-27T20:22:47

See a solution process below:

Because the $x$ value for both points are the same, $-2$ , we know the line going through these two points is a vertical line with the equation:

$x = -2$

For each and every value of $y$ , $x$ is equal to $-2$ .

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: $m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))$

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:

$m = (color(red)(4) - color(blue)(-2))/(color(red)(-2) - color(blue)(-2)) = (color(red)(4) + color(blue)(2))/(color(red)(-2) + color(blue)(2)) =6/0$

We can not divide by $0$ therefore the slope is undefined.