# Welcome to Algebra I: Representing a Direct Variation Algebraically and Graphically

33 minutes

Hi guys. Welcome to Algebra I. Today's lesson focuses on representing a direct variation algebraically and graphically. Your prior knowledge about the direct variation equation and graphing direct variation equations will help you get through this lesson. You ready to get started? Let's go. To jog your memory before we dive into this topic, recall what the equation of a direct variation looks like. There are two equations we can work with with direct variation. Either y equals kx or k equals y over x. Depending on the problem we're working with, sometimes one equation more helpful than the other. Remember that k was your constant variation, right? Keep that in mind. Let's keep going. Let's look at this one: example 1.

(female describer) Within a set of braces are three ordered pairs: minus 2 and minus 16, 3 and 24, and 4 and 32.

(teacher) Write an equation for the direct variation represented in the relation. In this situation, because we want to write that equation and we're not trying to determine if this is a direct variation-- we're not testing it out-- we're going to start by using-- We'll try to get to this. Let me scoot that so you can see. Our goal is to get to an equation in this form, y equals kx. What we need to determine is, what is k? Because we are told already that this is a direct variation, we don't need to test out those quotients like we do for each of these ordered pairs. We don't need to do negative 16 divided by negative 2, 24 divided by 3, and then 32 divided by 4 to ensure we get the same answer. We're told it's a direct variation situation, so we know we'll get the same answer. If you don't believe me, I'll show you just so you know. Negative 16 divided by negative 2 is 8; 24 divided by 3, it's 8; and 32 divided by 4-- let's get a little space here. It's 8, okay? When you're told that you have a direct variation situation, don't test your ordered pairs. You really just need to pick one--one ordered pair. What you want to find is, what is k? To write this equation, this y equals kx, I need to figure what is k? What is the constant variation? I proved already that this was a direct variation situation-- my testing out the ordered pairs-- so you can tell that k is 8. If k is 8 for this situation, then I can write the equation as y equals 8x. And I'm done, okay? To solve these problems where you write the equation, all you need to do is figure what is k and fill it in to that general format, that y equals kx, all right? Let's look at another one here. We have a table, but the directions are the same: "Write an equation for the direct variation represented in the relation." Kind of a mouthful.

(female describer) The ordered pairs in the table are minus 20 and minus 5, 28 and 7, and 44 and 11.

(teacher) What we want to figure is, what is k? Then we can write our direct variation equation. Because I'm already told this is a direct variation situation, I don't have to test every ordered pair. I'll just pick the first one. In order to figure out what k is, I need to do-- I'll write that here-- y equals k divided by x-- I'm sorry-- k equals y divided by x. For this one, k, if I pick the first ordered pair-- but you can choose any ordered pair-- y is negative 5; x is negative 20. I simplify this by dividing my numerator and my denominator by negative 5. Negative 5 divided by negative 5, positive 1. Negative 20 divided by negative 5 is positive 4. My k for this situation is 1 over 4. I want to write my equation in the format of y equals kx. Now that I know that k is 1/4, y equals 1/4x. Okay? And you're done. You have your equation for this direct variation situation, okay? If you chose to write your equation in this format-- the k equals y divided by x-- that's still acceptable. But when we're dealing with a table or set of ordered pairs, and eventually we get to the graphs, you want it in the y equals form most of the time. Both of these are acceptable if you were to have-- since your k is 1/4, you could say that 1/4 equals y divided by x. That is also true for this situation. Get in the habit of figuring what k is and then filling it in to that style of the equation. Okay, let's keep going here. I've got a couple for you. You have a set of ordered pairs and a table; you're asked to write that direct variation equation. Remember, figure what k is and then fill it in to that y equals kx equation. To check your answers, press play.

(describer) Relation A is a set of the three ordered pairs in braces-- 2 and 6, 5 and 15, and 9 and 27. Relation B is three ordered pairs in a table with two columns, headed x and y. The ordered pairs are 8 and 4, 10 and 5, and 18 and 9.

(describer) The cost of Suzanne's data plan varies directly with the number of gigabytes she uses. Last month, Suzanne used 6 gigabytes of data and was charged \$22.50. If Suzanne uses 8 gigabytes of data this month, how much will she be charged?

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In this program, students learn to represent a direct variation algebraically and graphically. They also learn to identify the relationship based on what a variation looks like on a graph. Part of the "Welcome to Algebra I" series.

## Media Details

Runtime: 33 minutes

Welcome to Algebra I
Episode 1
31 minutes
Welcome to Algebra I
Episode 2
25 minutes
Welcome to Algebra I
Episode 3
18 minutes
Welcome to Algebra I
Episode 4
17 minutes
Welcome to Algebra I
Episode 5
22 minutes
Welcome to Algebra I
Episode 6
9 minutes
Welcome to Algebra I
Episode 7
24 minutes