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Chapter 4: Problem 52

Can the equation of a vertical line be written in slope-intercept form? Explain.

Short Answer

Expert verified
No, a vertical line equation cannot be written in slope-intercept form because a vertical line has an undefined slope, and slope is necessary in the slope-intercept form.

Step by step solution

01

Identifying the characteristics of a vertical line

A vertical line goes straight up and down, thus it has no slope. When we talk about slope, we mean how much 'rise' there is for each unit of 'run'. Since a vertical line does not 'run' (move left or right), the concept of slope is not applicable to it -- the slope is undefined.
02

Understanding the slope-intercept form

The slope-intercept form of a linear equation is \( y = mx + c \), where \( m \) represents the slope, and \( c \) is the y-intercept. Clearly, slope is a fundamental part of this equation form.
03

Evaluating the possibility of a vertical line equation in slope-intercept form

Since the slope of a vertical line is undefined, and a slope value is needed for a slope-intercept form equation, we can conclude that the equation of a vertical line cannot be written in slope-intercept form.

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Most popular questions from this chapter

Determine the slope of the line. $$ y+3=-2(x-6) $$

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