Question

what is the equation of the line that passes through the point (6, -3) and has an undefined slope?

Explanation:

Step1: Recall slope types

A line with an undefined slope is a vertical line. The equation of a vertical line is of the form \(x = a\), where \(a\) is the \(x\)-coordinate of any point on the line.

Step2: Determine the value of \(a\)

The line passes through the point \((6, - 3)\). For a vertical line, the \(x\)-coordinate is constant. So the \(x\)-coordinate of the point \((6,-3)\) is \(6\), which means \(a = 6\).

Step3: Write the equation

Using the form \(x=a\) with \(a = 6\), the equation of the line is \(x=6\).

Answer:

\(x = 6\)