Question

find the slope of the line passing through the points (3,-9) and (3,9)

Answer 1

We find the slope as follows:

$m=\frac{9-(-9)}{3-(3)}\Rightarrow m=\infty$

So, the line is a vertical line.

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To find the slope of two points we use the following expression:

$m=\frac{y_2-y_1}{x_2-x_1}$

In this function, there are points (x1, y1) & (x2, y2).

If the values in the denominator are equal [As in the problem given] this means that the slope will be divided by 0 and therefore is not defined [Or infinite]. Since we can see that x1 = x2 that means that the line keeps moving but the x-coordinate of each point is located at x = 3 and the only values that vary are the y-components. The line given is the following:

So, its slope is undefined and that means the line is vertical.