Respuesta :

We can calculate the slope of a line knowing two of the points of the line as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

In this case, we have x1 = x2. Then the slope m would result in a quotient with denominator 0, as (x2 - x1) = 0.

[tex]m=\frac{2-(-4)}{-4-(-4)}=\frac{6}{0}=\text{undefined}[/tex]

In this case, the only line that passes through (-4,-4) and (-4,2) is a vertical line with equation x = -4.

Vertical lines have undefined slope (they are not even function like f(x), as they have multiple values of y for the same value of x).

Then, as the slope is the rate of change of y for a unit change in x, is undefined for vertical lines.

Answer: undefined.

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