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Horizontal and Vertical Lines

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[MUSIC PLAYING] Let's look at our objectives for today. We'll start by reviewing horizontal lines. We'll then review vertical lines. And finally, we'll do some examples graphing horizontal lines and vertical lines.

Let's start by reviewing horizontal lines. Here's an example of a horizontal line. Because it's horizontal, the y-coordinate is the same for all points on the line no matter what the value of x is. For example, if we look at two points on the line, negative 3, 2 and 4, 2, we can see that the y value is 2 at both points. Therefore, we can write the equation for the line as y equals 2 because the y value is always 2.

In general, all horizontal lines can be written as y equals a, where a is a constant value. Another important feature of horizontal lines is that the slope of all horizontal lines is 0, because there is no change in the y value between any two points on the line, and the numerator will always be 0 when calculating the slope between any two points on the horizontal line, as we can see from the formula.

Now let's look at vertical lines. Here's an example of a vertical line. Because it's vertical, the x-coordinate is the same for all points on the line no matter what the value of y is. For example, if we look at two points, 1, negative 5, and 1, 3, we can see that the x value is 1 at both points. Therefore, we can write the equation for the line as x equals 1, because the x value is always 1.

In general, all vertical lines can be written as x equals a, where a is a constant value. Another important feature of vertical lines is that the slope of all vertical lines is undefined because there is no change in the x value between any two points on the line. We can see from the formula that because the x values are always the same, the denominator will always be 0 when calculating the slope between any two points on a vertical line.

Now let's do some examples graphing horizontal and vertical lines. Here's an equation. We have y equals negative 3. We know that this will be a horizontal line because the y value will be negative 3 for all points on the line. And the graph will go through negative 3 on the y-axis. So to graph, we find negative 3 on the y-axis and we draw a horizontal line through the point.

Let's look at another example. This time we have x equals negative 4. We know that this will be a vertical line because the x value will be negative 4 for all points on the line. And the graph will go through negative 4 on the x-axis. So to graph, we find negative 4 on the x-axis and we draw a vertical line through the point.

Let's go over our key points from today. Make sure you get these in your notes so you can refer to them later. The y-coordinate for all horizontal lines is the same no matter what the value of x is. All horizontal lines can be written as y equals a, where a is a constant value. And all horizontal lines have a slope of 0.

The x-coordinate for all vertical lines is the same no matter what the value of y is. All vertical lines can be written as x equals a, where a is a constant value. And all vertical lines have a slope that is undefined. So I hope that these important points and examples helped you understand a little bit more about horizontal and vertical lines. Keep using your notes and keep on practicing and soon you'll be a pro. Thanks for watching.

Formulas to Know

- Slope for Horizontal Lines
- Slope for Vertical Lines