What is the equation of a line that passes through the point (2,1) and has an undefined slope?

Solution:

Given that, the equation of the line is with an undefined slope and goes through the point (2,1).

⇒ If the line has an undefined slope then the line is parallel to the y-axis (perpendicular to the x-axis).

We have the equation of the line passing through (h, k) and perpendicular to the x-axis as,

x = h

Here, given that, (h, k) = (2, 1)

∴ The required equation will be x = h ⇒ x = 2.

Note: If the line has slope zero and passes through the point (h, k) then its equation is y = k.

What is the equation of a line that passes through the point (2,1) and has an undefined slope?

Summary:

The equation of the line with an undefined slope and going through a point (2,4) is x = 2.