# Vertical and Horizontal LinesI actually teach high school math but I am so amazed how much my students get vertical and horizontal lines mixed around. They also confuse the idea of no slope and...

I actually teach high school math but I am so amazed how much my students get vertical and horizontal lines mixed around. They also confuse the idea of no slope and undefined slope. I was just curious if you guys run into this in middle school and how you help them understand the difference.

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Can you relate it to the "rise over run" definition? When you do that, you get a vertical line slope as a fraction with a denominator of zero, which they should already know as an undefined concept.

In my class, when we first cover slope, I tell the students that there is a little man who lives on the left side of their paper. We even draw him on the side of our graph. When he gets to the line, we use him to help us with the slope.

If he is going uphill: positive slope

If he is going downhill: negative slope

When he gets to a horizontal line he always says "Oh, this is easy" and his mouth is in the shape of an O - which is our slope of 0.

When he gets to the vertical line, he decides it is impossible, so that is the undefined slope.

Also, when we study the equations for vertical and horizontal lines, I found that my students were often getting confused on which was which. Whenever we see an equation like x=2, we say "I'm so eXcited, jump up and down!" Now my students almost always get those graphs correct.

I can't agree more than the analogy to an airplane by Post #4. It really hits home about slope.

Yes. Vertical, going up, moving up, raising high,flying high,reach the sky,attain the height are all some of the synonimns that communicate the vertical sense.

The sense of opposite direction like , vertically down, below,going down, a fruit falling down are to be flashed to the young mind to create the sense of downward direction.

If you see** horizontally** an early morning,enjoy the sight of sun in an appeasing red colour and so in the in the evening wearing the same red robe again.But in the mid day see the same sun frying us from **vertically** above our head.

I hope a panoramic and picturesque nature helps create the awareness of horizontal and vetical in sense.

If I remember right, the concept of vertical and horizontal was explained to me by my teacher, about 55 years back, by giving example of a person standing erect as vertical, and a person lying down as horizontal.

If I have to explain this concept to young children today, I would use this analogy.

All spatial imagination comes to a curious student whose teacher is his own interest.The real teacher is the one who can inspire that interest in the student.

Vertical , horizontal ,the cardinal directions are all the spacial awareness.

The perpendicular displacement to the plane of gound is the height - some of the words that I can tell. And the horizontal is the displacement parallel to the ground.

Slope is the ratio of perpendicular displacement to the the one parallel to the ground.

The slope is a ratio or rate of displacement in height to the ground parallel displacement.

in response to the original question: How do I teach the students the difference between VERTICAL SLOPE and HORIZONTAL SLOPE. I use the analogy of an airplane. Always read the line from LEFT to RIGHT.

(+) slope - plane is taking off (/)

(-) slope - plane is landing (\)

(0) zero slope - the plane has reached its maximum height and is cruising

(|) undefined slope - UH-OH! the plane has lost its power, it is spirling straight down. I stress that in reality it is a negative slope.

Hope this helps!

Can you relate it to the "rise over run" definition? When you do that, you get a vertical line slope as a fraction with a denominator of zero, which they should already know as an undefined concept.

I relate to students four different scenarios: a positive slope, a negative slope, a zero slope and an undefined slope. From the first illustration of a line, make sure always begin from left=then upward movement for a positive slope. then draw another line, begin left and move downward for a negative slope. then explain the RISE (+), FALL (-) and the RUN, the line on a level plane. From that level line, illustrate perpendicular lines (90 deg) showing the vertical and horizontal, or better review the X-axis and Y-axis formation for the horizontal(X =left to right movement) and the vertical(Y = up and down movement.) Recall PARALLEL. Any line parallel to the X-axis has a zero slope, since it doesn't RISE nor FALL, always on a level. Any line parallel to the Y-axis is undefined because there is a rise or fall but the run (origin) is always on 0, hence undefined. (Sorry quite long explanation)