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Chapter 2: Problem 96

Explain how to graph the equation \(x=2 .\) Can this equation be expressed in slope-intercept form? Explain.

Short Answer

Expert verified
The line \(x = 2\) is a vertical line passing through all points where the x-coordinate is 2. It cannot be expressed in slope-intercept form because it does not describe a relationship between x and y, which is a key requirement in the slope-intercept form (\(y = mx + b\)).

Step by step solution

01

Identifying the line

The given equation is \(x = 2\). It represents a vertical line in a two-dimensional plane passing through points where x-coordinate is always 2.
02

Graphing the line

To graph this line, take a graph paper or a coordinate graph. Locate on the x-axis where \(x = 2\) and plot a point there. Since it's a vertical line, this line extends upwards and downwards from this point. Sketch the line moving straight up and straight down from the plotted point.
03

Examining the slope-intercept form

The slope-intercept form of the equation of a line is \(y = mx + b\) where m represents the slope of the line and b is the y-intercept. Since the equation \(x = 2\) doesn't show a relationship between the x and y variables (meaning, there is no y variable present), it cannot be expressed in slope-intercept form.

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