Flat or Vertical Through

Through any one point there is only one flat line and only one vertical line. You can write both equations straight from the point. The flat line through (2, 5) has every point at height 5, so its equation is $y = 5$. The vertical line through (2, 5) has every point at x-coordinate 2, so its equation is $x = 2$.

The flat and the vertical line through (2, 5)

Point-slope form also works for the flat line, because its slope is 0. Substituting $m = 0$ and the point (2, 5) gives $y-5 = 0\left(x-2\right)$. The right side is 0, so $y = 5$. Point-slope form cannot give the vertical line, because a vertical line has no slope to substitute. Write its equation directly as $x = 2$.