Final answer:
The equation of a vertical line passing through the point (6,3) is x = 6, as it represents a line where all points have an x-coordinate of 6. Therefore, the correct answer is option b) x = 6.
Step-by-step explanation:
The equation of a vertical line is one where all points on the line have the same x-coordinate. For a line to pass through the point (6,3), the line must have all points with an x-coordinate of 6. Therefore, the equation representing this vertical line is x = 6.
This equation indicates that no matter what the value of y is, the value of x will always be 6, creating a line that is perfectly vertical and crosses the x-axis at the point (6,0).
It is important to note that vertical lines do not have a slope because they go straight up and down, and therefore the concept of “rise over run” does not apply as the run would be zero, leading to division by zero, which is undefined.
A vertical line has an equation of the form x = c, where c is the x-coordinate of any point on the line. In this case, the line passes through the point (6,3), so the equation is x = 6. Therefore, the correct answer is option b) x = 6.