Final Answer:
The vertical line through the point (-6,4) is x = -6.
Step-by-step explanation:
To find the equation of a vertical line through any given point, you must understand what defines a vertical line in a two-dimensional Cartesian coordinate system:
1. A vertical line is one where all points on the line have the same x-coordinate, regardless of their y-coordinate.
2. Vertical lines have an undefined slope since they do not run horizontally at all—their change in x is 0, which would make the denominator in the slope formula (which is "change in y" over "change in x") equal to zero, and division by zero is undefined.
3. The equation of a vertical line is very simple, it is always of the form: x = a, where "a" is the x-coordinate of any point the line passes through.
Given the point (-6,4), the x-coordinate of this point is -6. Therefore, the equation of the vertical line that passes through (-6,4), and indeed any other point with an x-coordinate of -6, is:
x = -6
There is no y-component to the equation of a vertical line because the y-value can be anything. Every point on this line will have an x-value of -6, no matter what the y-value is.