Vertical Lines

You are able to move the line by clicking on and moving point J. Please answer the questions to the right.

Athena Matherly, November 10, 2006, Created with GeoGebra

1. Which axis is the red line crossing? At what point is the line crossing the axis?
2. Move the blue slider to 1, what is the name and coordinates of the point that appears? Do the same by moving the slider to 2,3, and 4.
3. What do you notice about the coordinates of these points?
4. Using the answers from the above questions, make a guess as to what the equation of this line is. Move slider 2 to the right to check your answer.
5. Move slider 2 back to the left. Use point J to move the line along the axis. Stop at any point and write the equation of the point you stopped at along with the equation of this line. Check your answer by moving the blue slider.
6. Use any combination of two points that lie on the line to find the slope using the slope formula (y₂-y₁)/(x₂-x₁). Form a conclusion about the equation of vertical lines and their slopes.