Questions: What is the slope of the line that passes through the points (6,-8) and (6,-3)? Write your answer in simplest form.

Solution Steps

To find the slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

In this case, the points are \((6, -8)\) and \((6, -3)\). We substitute these values into the formula to find the slope.

The points given are \((6, -8)\) and \((6, -3)\).

The slope \(m\) of the line passing through the 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 the values:

\[ m = \frac{-3 - (-8)}{6 - 6} = \frac{-3 + 8}{0} = \frac{5}{0} \]

Since the denominator is zero, the slope is undefined. This indicates that the line is vertical.

Final Answer