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 $\infty$.
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