Slope Calculation for Vertical Lines

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

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

Given the points are $(3, -2)$ and $(3, 4)$. We can assign:

• $(x_1, y_1) = (3, -2)$
• $(x_2, y_2) = (3, 4)$

Substitute the coordinates into the slope formula:

$m = \frac{4 - (-2)}{3 - 3}$

Simplify the expression:

$m = \frac{4 + 2}{0}$

$m = \frac{6}{0}$

Division by zero indicates an undefined slope. For a line, this occurs when the line is vertical. An undefined slope is represented as infinity ($\infty$).

Thus, the slope of the line passing through the points $(3, -2)$ and $(3, 4)$ is $\infty$.