What is the slope of the line that passes through the points (-9, -9) and (-9, -7)? Write your answer in simplest form.

Understand the Problem

The question is asking for the slope of the line that passes through two given points: (-9, -9) and (-9, -7). The slope formula is used to determine how steep the line is between these points.

Answer

The slope is undefined.

Steps to Solve

Identifying the Points

We have two points:

Point 1: $(-9, -9)$
Point 2: $(-9, -7)$

Using the Slope Formula

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

Substituting our points into the formula: $$ m = \frac{-7 - (-9)}{-9 - (-9)} $$

Calculating the Values

Now we calculate the values:

For the numerator: $$ -7 - (-9) = -7 + 9 = 2 $$
For the denominator: $$ -9 - (-9) = -9 + 9 = 0 $$

Now substitute these values back into the slope formula: $$ m = \frac{2}{0} $$

Determining Undefined Slope

Since division by zero is undefined, the slope of the line is undefined. This indicates that the line is vertical.

The slope of the line is undefined.

More Information

A vertical line has an undefined slope because there is no horizontal change between the points, even though there is a vertical change. This concept is essential in understanding the nature of linear relationships.

Tips

Some may mistakenly think that the slope is zero if the points have the same $x$-coordinate. Remember, the slope is undefined when the denominator (the difference in $x$ values) is zero.

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