Horizontal lines have no vertical change -- it continues straight left or right. In other words, the change in the y values between any points on the graph is 0, since there is no change. This means that the slope of a horizontal line is 0 (m=0). Vertical lines do not have a horizontal change; the line goes straight up and down. In other words, the change in the x values between any points on the graph is always 0, which would make the denominator of the slope 0. Since anything divided by 0 is undefined, the slope of a vertical line is undefined. An easy way to remember the difference is that the word horizontal has a "z" in it, just like the word zero.
This graph has two lines and I’m asked to find the slope of each one. So for some students, they have some interesting things memorized about slopes of vertical and horizontal and vertical lines, and they’d be able to look at this and write the answer just based on what they have memorized, we’ll get back to that in a second. What a lot of students would do, would be to try to draw a slope triangle or try to find two points that the line goes through and use the slope formula.
Here is what I mean, look at line one, I could use any point I want to along this line and try to draw a triangle or put them into the slope formula, but when I tried that I would see that my vertical change is zero, right this one is horizontal like a flat line, there’s no change up and down it, there’s no vertical change. That’s why no matter what fraction, or no matter how I try to write this as a fraction, I would have zero in the numerator. If I had a zero in the numerator of a fraction that means the fraction is going to be equal to zero. By the way, that’s true for every single horizontal line. Any line that’s flat like that, the slope will always be zero.
Now don’t get that confused with what we’ll see next. This is a vertical line. Vertical lines do have a vertical change, but they don’t have a horizontal change. What that means is you would have zero in the denominator of your slope ratio, and that’s not allowed in Math, it’s what’s called undefined. So the slope for line 2, or any vertical line would be undefined, slope is undefined or you might write the words, no slope, either one of those is okay. And that’s kind of funny because usually in Math our answers are numbers and this time we got answers that were word, don’t worry it’s still correct.
So if you want to be a superstar and get these really quick, try just memorizing always, always, always the slope of a horizontal line is zero, and the slope of a vertical line is always undefined.
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