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
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Parallel and Perpendicular lines

 
 
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
AVAILABLE MASTERED IN PROGRESS

(MAX is 24; there are 24 different problem types.)