Questions: Find the slope of the line that goes through the given points. (5,-2) and (5,-3) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is (Simplify your answer. Type an integer or a fraction.) B. The slope of the line is undefined.

Solution Steps

To find the slope of a line that goes through two given points, we use the slope formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Given the points (5, -2) and (5, -3), we can substitute these values into the formula. If the x-coordinates are the same, the slope is undefined.

1. Identify the coordinates of the two points.
2. Substitute the coordinates into the slope formula.
3. Check if the x-coordinates are the same to determine if the slope is undefined.

We are given two points: \((5, -2)\) and \((5, -3)\).

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points into the formula: \[ m = \frac{-3 - (-2)}{5 - 5} = \frac{-3 + 2}{0} = \frac{-1}{0} \]

Since the denominator is zero, the slope is undefined.

Final Answer