Q.Find the equations of the lines through the point $(5, -2)$ that are

[!TLDR] The y-coordinate stays fixed for the line parallel to the x-axis, and the x-coordinate stays fixed for the line parallel to the y-axis. [!A …

A line through $(5,-2)$ parallel to the x-axis has every point sharing the same y-coordinate as $(5,-2)$, namely $-2$; its equation is $y=-2$. A line through the same point parallel to the y-axis has every point sharing the same x-coordinate, namely $5$; its equation is $x=5$. Thes …

Read the fixed coordinate directly off the given point: the y-coordinate for the horizontal lin …

A common slip is swapping the two — writing $x=-2$ for the horizontal line or $y=5$ for the vertical one; remember a line parallel to the x-axis is a HORIZO …