Q. 4.33 - Elementary Statistics

Question

Vertical Lines. In this section, we stated that any nonvertical line can be described by an equation of the form $y=b_0+b_{1}x$.

a. Explain in detail why a vertical line can't be expressed in this form.

b. What is the form of the equation of a vertical line?

c. Does a vertical line have a slope? Explain your answer.

Step-by-Step Solution

Answer

(a) A vertical line has no slope

(b) The form of the equation is, $x=k$

(c) It has no slope.

Part (a) Step 1: Given information

We are given that any nonvertical line is given as, $y=b_0+b_{1}x$

Part (a) Step 2: Explanation

The vertical line can not be expressed in the given form of the equation because it has no slope (existing) this is due to the reason $x$ increments by 1, we cannot determine how much the vertical line rises.

Part (b) Step 1: Given information

We need to find the form of equation of vertical line.

Part (b) Step 2: Simplify

A vertical line has only one $x$-value that is possible.

Hence the line has the equation of the form,

     $x=k$

Here, $k$ is constant 

Part (c) Step 1: Given information

We need to find the slope of equation

Part (c) Step 2: Explanation

From part (a)

It is clear that vertical lines have no slope.