is-every-linear-function-a-direct-variation

Name: is every linear function a direct variation
Uploaded: 2020-08-17
Duration: 1 min 1 s
Channel: Numerade
Description: Is every linear function a direct variation?

Question

Is every linear function a direct variation?

Yemi Uthman · Accepted Answer

for this question. We want to know. Every linear function is also a direct variation. Creation some what we already know this After recreation equations fall, the form y equals K X. Only the equations for the form black was MX plus B. So you can see from this is that they fold the same form except K. Here is M here, so I will say direct variation were rewrite as y equals MX and linear equations will be. Why equals X Plus B? So we&#x27;ll see that a linear equation is also direct variation equation on Lee If if and only if, b equals equals does not equal a Loretta&#x27;s be equals zero, so therefore not all linear equations, our direct creations.

Emma Chickles · Answer

and this problem where Asif of the direct variation of two variables, means that this is a linear function. To do this, we&#x27;ll need to look at the definition of a direct variation for a direct variation of two variables and must be true that the ratio between two variables is constant. This is also this also must be true for a linear function, So a direct creation of two variables is a linear function.

Cory Kuzinski · Answer

So with direct variation, it&#x27;s why equals K times acts. But if you divide both sides by axe here, you also get this ratio. Why, okay, equals why over acts. So that means that if every single time you mult a divide, why by actually is that the same thing? Then then, yes, you do have truck variation. So we have this table of X and Y values when X is negative too wise One when x is to y eyes negative one. And when X is four, why is negative too? So I&#x27;m gonna add another column here, and I&#x27;m gonna call it why over X and we&#x27;re gonna check and see. So one divided by native to is negative 1/2 negative, one divided by two is negative. 1/2 and negative two divided by four is also negative 1/2. So, um, does it very directly will answer that first, why does very directly with X Andi Since it does, we&#x27;re also gonna write the equation. So that equation is gonna be, um why equals negative 1/2 times X. Why does very directly with X y equals negative? 1/2 times X is our drug variation equation. You could check that too, you know, Negative 1/2. Um, times Negative too. Is positive. One negative. 1/2 times. Positive too is negative. One negative. Half of four is negative too. So it works.

Jeffrey Morris · Answer

so there&#x27;s one notable example of a straight line that it&#x27;s not represent a function, and that is when we have a line that a straight vertical 100% do you think about right now? If we let&#x27;s just say that we have our graph but like this, this these air, actually and then the line is sitting cure at are actually quite a positive one that we have our equation X is the core to one right here We have ecstasy, Goto one, we can&#x27;t have an equation wise. You could have an extra place to be when we don&#x27;t have a Why so even though we have a straight line, we cannot have any equation from this where we have a why. So why would just increase at a constant at any rate and that you can&#x27;t have but one X value, which is one. So this would not be a linear function out here, even though we have a straight line

Charles Carter · Answer

So this problem gets a, um, an issue are do all in your functions, um, have in verses. So as far as all linear functions, we can say no. Um, that&#x27;s because there is a linear function. Why equals a, um that is not 1 to 1. Said&#x27;s, um so that means there is no inverse other than that most other linear functions, I guess. Also, if he had X equals B, um, but then it&#x27;s not a function, so that&#x27;s not part of this list. Um, so every other linear function, though, would have a number. So other than these two major problems, the other linear functions, except for why equals a that they do have in versus because they are 1 to 1. Okay. Thank you, very.

Charles Carter · Answer

Okay, So if this problem were given some values for X and y want to deter? Asked to determine if it&#x27;s a direct or inverse variation relationship, our ex values Air 73 Lauren and one Death and an R Y values are 17 1/3 one and five. So quick ways to tell if it&#x27;s on direct or in verse. It&#x27;s a direct relationship. We would have a constant quotient of lying ex, which is equal to okay, value. And for in inverse we have the product of X and Y is equal to a constant. So this case, I can quickly see that five. Multiply all the X&#x27;s and y&#x27;s the seven times 173 times 1/3 1 times one I&#x27;m gonna get a constant value of one and solving for why I&#x27;ll give Why Just dividing both sides by X r K body was one. And so for me it would just be Why equals whatever acts, thank you very much. That was an inverse relationship, uh, with the formula y equals one over axe. Thank you very much.

Problem

Is the direct variation of two variables always a…

Problem 21 Medium Difficulty

Is every linear function a direct variation?

Answer

Not all linear equations are direct variations.

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Not all linear equations are direct variations.

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Ann Xavier GantertAlgebra 2 and Trigonometry

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Algebra 2 and Trigonometry