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Chapter 1: Problem 20

Find the slope and \(y\) -intercept (if possible) of the equation of the line. Sketch the line. $$x+5=0$$

Short Answer

Expert verified
The slope of the line \(x + 5 = 0\) is undefined and it doesn't have a \(y\)-intercept. The line is vertical and is represented on a graph as a line passing through \(x = -5\).

Step by step solution

01

Identify the Form of the equation

The given equation is \(x+5=0\). This is obviously in the format of vertical line equation \(x = c\), where \(c\) is a constant.
02

Find the Slope and \(y\)-intercept

For vertical lines of the form \(x = c\), the slope is undefined because the change in \(x\) is zero. This means the line is perfectly vertical and does not 'rise' or 'run'. A \(y\)-intercept does not exist for a vertical line as it does not cross the y-axis.
03

Sketch the Line

Since the equation is \(x + 5 = 0\), the line passes through \(x = -5\). Any point on this line will have \(-5\) as its x-coordinate. To sketch this line, simply draw a vertical line through \(x = -5\) on a graph.

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