To find the equation of a line that passes through the point [tex]\((-6, -7)\)[/tex] and has an undefined slope, we must understand what an undefined slope signifies.
1. Undefined Slope:
A line with an undefined slope is a vertical line. A vertical line does not tilt to either side; it goes straight up and down.
2. Characteristics of a Vertical Line:
As a vertical line is perfectly aligned along the y-axis, it does not have a traditional slope value which we can express in numerical form.
3. Equation of a Vertical Line:
The equation of a vertical line passing through any point [tex]\((a, b)\)[/tex] is written as:
[tex]\[
x = a
\][/tex]
This form indicates that no matter what the y-coordinate is, the x-coordinate always remains constant at [tex]\(a\)[/tex].
4. Applying the Given Point:
In this problem, the vertical line passes through the point [tex]\((-6, -7)\)[/tex]. Therefore, the constant x-coordinate for the vertical line is [tex]\(-6\)[/tex].
Thus, the equation of the line that passes through [tex]\((-6, -7)\)[/tex] and has an undefined slope is:
[tex]\[
x = -6
\][/tex]
