Question

select the correct line. which line is perpendicular to $overleftrightarrow{ab}$?

Explanation:

Step1: Recall perpendicular - line property

Two lines are perpendicular if the product of their slopes is - 1. First, find the slope of line AB. Let \(A=(0, - 6)\) and \(B=(2,-8)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So, the slope of line AB, \(m_{AB}=\frac{-8+6}{2 - 0}=\frac{-2}{2}=-1\).

Step2: Find the slope of the perpendicular line

If the slope of line AB is \(m_{AB}=-1\), and the slope of a line perpendicular to it is \(m\), then \((-1)\times m=-1\), which gives \(m = 1\).

Step3: Identify the line with slope 1

We need to find the line among line 1, line 2, line 3, and line 4 with a slope of 1. The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope. A line with a slope of 1 has a "rise - over - run" of 1. By observing the lines on the graph, we can see that line 4 has a positive slope and for every 1 unit increase in \(x\), there is a 1 unit increase in \(y\).

Answer:

line 4