Question

answer attempt 2 out of 2
original slope: undefined
parallel slope: undefined

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For a vertical line, if we take two points $(x_1,y_1)$ and $(x_2,y_2)$ on the vertical line, $x_1=x_2$.

Step2: Calculate original slope

Let the vertical line pass through points $(x_1,y_1)$ and $(x_2,y_2)$ with $x_1 = x_2$. Then $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{y_2 - y_1}{0}$, which is undefined.

Step3: Determine parallel - slope property

Parallel lines have the same slope. Since the original line is vertical and has an undefined slope, any line parallel to it is also vertical and has an undefined slope.

Answer:

Original Slope: undefined
Parallel Slope: undefined