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High School Precalculus: Homework Help Resource32 chapters | 273 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After reading this lesson, you will see just how easy it is to graph the equation y=0. You'll learn why the graph looks the way it does and how you can check to make sure you did it right.

In math, a **graph** is a visual representation of how the variables in an equation relate to each other. You can go about graphing the equation y=0 in two different ways. We'll review the steps for both ways in this lesson.

The first method involves using the **slope-intercept form** of a linear equation. Your equation y = 0 is a linear equation since the variable has no exponent. Remember, the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Using this method, the steps are as follows:

- 1. Write out the equation in slope-intercept form using zeroes as necessary.
- 2. Label your slope and y-intercept.
- 3. Plot your y-intercept.
- 4. Find your next point by using the slope.
- 5. Connect your points.

The second method involves plotting several points to see how the graph behaves. Let's go through those steps now.

- 1.
**Plug in several values**for x and then find what y equals. You can use x = -2, x = -1, x = 0, x = 1, and x = 2. - 2. Plot the points you found.
- 3. Connect the dots to find your graph.

Now, let's go ahead and graph your equation y = 0. We'll do it both ways so you can see how both work out. Once you know both ways, you can choose the one that is easiest for you.

First way involves using the slope-intercept form y = mx + b. Let's go. Step one is writing out the equation in slope-intercept form.

- Rewriting y = 0 in slope-intercept form, you get y = 0x + 0.
- Label your slope as 0 and your y-intercept as 0.
- Plot your y-intercept. The y-intercept is 0, so you place a dot at the point (0, 0).
- Find your next point by using the slope. The slope is 0, so this tells you that no matter how far you go to the left or right, your y value will always be 0. So you go one space to the right for x = 1. Since your slope is 0, your y value is still 0; it doesn't go up or down. Your next point is (1, 0).
- Connecting your points. You connect your two dots with a line and you get your graph of y = 0.

And you are done!

Let's try the second way to see how that works.

1. You're plugging in x = -2, x = -1, x = 0, x = 1, and x = 2. Remember, this is a linear equation, so there is an x variable in there. It's just hidden because it is being multiplied by a 0, as you saw when you wrote out the whole slope-intercept form in the previous way to solve this problem. That x is where you'll be plugging in your values. So, plugging them in, you get this:

x | y |
---|---|

-2 | 0 |

-1 | 0 |

0 | 0 |

1 | 0 |

2 | 0 |

2. You go ahead and plot all these points on the graph.

3. You then draw a line through all these points.

And there's your graph!

There is a shortcut to doing this problem if you remember that a slope of 0, which is what this problem has, will always give you a horizontal line. If you know this, then you can simply just go ahead and draw a horizontal line through the y-intercept, in this case 0. Since the equation y = 0 has a y-intercept of 0, your graph is essentially the x-axis.

Let's try an example.

Eric is performing a study of girls and spiders. He is seeing if the number of spiders present changes how girls feel about spiders. The y-axis in his study represents how much the girls like the spiders. A y value of 0 means the girls don't like the spiders and never will. An x value of 1 means 1 spider, an x value of 2 means 2 spiders. His research found that no matter how many spiders there are, the girls always said they dislike the spiders. The y-value is always 0. Eric sees that his data follows the graph of y=0. Graph this equation.

You see that this problem is asking you to graph the equation y=0. You did well if you remembered that this equation graphs into a horizontal line passing through the y-axis at 0.

To review, there are two methods you can use to graph y=0: the **slope intercept form** and **plugging in values**. But you can also remember a shortcut, which is that a slope of zero will always be represented as a horizontal line and therefore, when y=0, the graph will essentially show a line through the x-axis.

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High School Precalculus: Homework Help Resource32 chapters | 273 lessons

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