HORIZONTAL AND VERTICAL LINES
Vertical Lines
 The points $\,(x,y)\,$ that satisfy the equation $\,x = 3\,$ (that is, $\,x + 0y = 3\,$) are all points of the form $\,(3,y)\,$, where $\,y\,$ can be any real number. This is the vertical line that crosses the $\,x$-axis at $\,3\,$. That is, in order to satisfy the equation $\,x =3\,$, the $\,x$-value of a point must be $\,3\,$. The $\,y$-value can be anything it wants to be. To get to any of these points from the origin, you move $\,3\,$ units to the right, and then up/down to your heart's content. As a memory device, you might think of exaggerating the first stroke of the $\,x\,$ to make a vertical line. Memory Device for Vertical Lines
Horizontal Lines
 The points $\,(x,y)\,$ that satisfy the equation $\,y = 3\,$ (that is, $\,0x + y = 3\,$) are all points of the form $\,(x,3)\,$, where $\,x\,$ can be any real number. This is the horizontal line that crosses the $\,y$-axis at $\,3\,$. That is, in order to satisfy the equation $\,y =3\,$, the $\,y$-value of a point must be $\,3\,$. The $\,x$-value can be anything it wants to be. To get to any of these points from the origin, you must move up $\,3\,$ units; you can move left/right to your heart's content. As a memory device, you might think of exaggerating the $\,y\,$ to make a horizontal line. Draw a rising sun to remind you of the horizon! Memory Device for Horizontal Lines
HORIZONTAL and VERTICAL LINES
Let $\,k\,$ be a real number.

Equations of the form $\,x = k\,$ graph as vertical lines.
The $\,y$-axis is a vertical line; its equation is $\,x = 0\,$.
All other vertical lines are parallel to the $\,y$-axis.
All vertical lines are perpendicular to the $\,x$-axis.
Vertical lines have no slope; i.e., the slope is not defined.

Equations of the form $\,y = k\,$ graph as horizontal lines.
The $\,x$-axis is a horizontal line; its equation is $\,y=0\,$.
All other horizontal lines are parallel to the $\,x$-axis.
Horizontal lines are perpendicular to the $\,y$-axis.
Horizontal lines have slope $\,0\,$ (zero).
EXAMPLES:
Question:
Write the equation of the horizontal line that passes through the point $\,(3,-2)\,$.
Answer: $y = -2$
Question:
Write the equation of the line through $\,(3,-2)\,$ that is perpendicular to the $\,x$-axis.
Answer: $x = 3$
Master the ideas from this section