The Graphs of Horizontal and Vertical Lines 05:30 minutes

Video Transcript

Transcript The Graphs of Horizontal and Vertical Lines

Stephanie is really into old school computer gaming. So she's learning how to program to make her own game. In order for Stephanie to make her character, 8bitbot, move along the correct paths, she needs to investigate the graphs of horizontal and vertical lines. Let's start by first setting up a coordinate plane. We'll draw and label the x-axis and then the y-axis. Let’s examine the horizontal line Stephanie wants 8bitbot to move along. By examining a few points along this horizontal line, we can write an equation to describe it. Let's pick some random ordered pairs: negative 5, negative 2; negative 3, negative 2; zero, negative 2; and 2, negative 2. Do you notice a pattern? Though the x-values change, the y-values are all the same at negative 2. So, the equation of this horizontal line is 'y' equals negative two. What other qualities does this horizontal line have? The line is parallel to the x-axis. This means it will never touch the x-axis, and therefore, has no x-intercept. It does, however, have a y-intercept at zero, negative 2 and is perpendicular to the y-axis. Additionally, do you notice anything about the slope of this horizontal line? There doesn’t seem to be an incline at all. So, let’s examine that by taking two points from the line and substituting them into the slope formula. Remember, the formula to find slope is 'y' two minus 'y' one over 'x' two minus 'x' one. We'll use the points negative 5, negative 2 and negative 3, negative 2, to calculate the slope. That gives us zero divided by two. But wait! Remember, zero divided by anything is zero, so the slope, m, equals zero. Stephanie understands the horizontal line and enters the rule ‘y' equals negative two into her program. And 8bitbot is off! But there’s another direction that he needs to move. So, let's investigate this vertical line of the ladder. Like we did with the horizontal line, we can pick and label some random points on the line. Do you see a pattern in these ordered pairs? Similar to the horizontal line where the y-values didn't change, we can see that the x-values don't change when the line is vertical. Therefore, we can write the equation as 'x' equals five. What other qualities does this vertical line have? This vertical line is parallel to the y-axis which is another vertical line, so it won't have a y-intercept. However, it has an x-intercept at the point five, zero and is perpendicular to the x-axis which is a horizontal line.
The vertical line is also perpendicular to our horizontal line from the first example. So, what does that mean for the slope of the vertical line, or actually all vertical lines? Let's examine this slope algebraically by again using the slope formula and any two points from the line. This results in negative one over zero. Whoa!!!! Wait a minute! We can’t divide something by nothing. Therefore, this slope is undefined. In fact, all vertical lines have an undefined slope because there is no difference in the x-values. Phew. That's good to know.
Stephanie types in 'x' equals 5 to make 8bitbot move vertically. Look at him go! Before Stephanie finishes her programming, let's review. Our first example was a horizontal line with the equation 'y' equals negative two. Let's look at a few more horizontal lines. All horizontal lines can be written as 'y' equals some constant. There is no 'x' term in horizontal lines because the slope is always zero. The slope of any horizontal line is always zero, because the numerator is zero because there is no change in the y-values. Our vertical line's equation was written as 'x' equals 5. This is the opposite when compared to horizontal lines, as all vertical lines can be written as 'x' equals some constant. Vertical lines have no 'y' term in the equation. No matter what vertical line you have, the slope will always be undefined because there is a zero in the denominator.
This means there is no difference because there is no change in the x-values. Understanding the characteristics of horizontal and vertical lines has helped Stephanie program the correct code for 8bitbot's movements. So, what’s 8bitbot doing now? Oh, poor Stephanie. It must be late.