Horizontal lines in the coordinate plane represent situations where the $y$-value doesn’t change at all while the $x$-value changes.

The horizontal line that goes through the point $(0,3)$ can be described by saying that “for all points on the line, the $y$-value is always 3.” Since horizontal lines are neither increasing or decreasing, they have a slope of 0, and so an equation for this horizontal line is $y=0x+3$, or just $y=3$.

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Vertical lines in the coordinate plane represent situations where the $x$-value doesn’t change at all while the $y$-value changes.

The vertical line that goes through the point $(\text{-}2,0)$ can be described by saying that “for all points on the line, the $x$-value is always -2.” An equation that says the same thing is $x=\text{-}2$.