Question

What is the equation of a vertical line passing through the point (−4, 7)?

A) y = 7
B) y = -4
C) x = 7
D) x = -4

Answer 1

the vertical line will pass through the x coordinate of the given point.

Answer 2

Start with a simple coordinate plane.

Answer 3

y will not be a part of the equation

Answer 4

As an example, what do we know about a vertical line that passes through (2, 0)?

Answer 5

What we know about it is that every x-coordinate is 2.
Every point on the vertical line through (2, 0) has x-coordinate 2.
Here are some points on that vertical line: (2, 0), (2, 10), (2 -5), (2, 80), (2 -1000)
In other words, I don't care what y is. Every x-coordinate is 2.
Then the equation is simply x = 2.
The equation does not have a y in it because no matter what y is, x is always 2.

Now look at your own question.
Since you are given a point on the line, you know that every point on that vertical line will have the same x-coordinate as your given point.
What is the equation?

Answer 6

x=a is a vertical line
where a is any real number.