Question

analyze why is the slope undefined for vertical lines? explain. the difference in the select choice is always 0, and select choice by 0 is undefined. select choice x-values y-values

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Analyze vertical lines

For a vertical line, all points on the line have the same \( x \)-value. So, \( x_2 - x_1 = 0 \) (the difference in \( x \)-values is 0).

Step3: Analyze division by zero

In the slope formula, we have a division by \( x_2 - x_1 \). Since division by 0 is undefined in mathematics, when \( x_2 - x_1 = 0 \) (as in vertical lines), the slope is undefined. So the first blank is "x - values" and the second blank is "dividing".

Answer:

The difference in the \(\boldsymbol{x\text{-values}}\) is always 0, and \(\boldsymbol{\text{dividing}}\) by 0 is undefined.