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Algebra Readiness Fall Question help

 
 
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Algebra Readiness Fall Question help
by Celena Meng - Thursday, October 24, 2019, 2:31 PM
 

I need help with 6-6 Practice Skills. (Chapter Six) 

For the exercises 1-3, determine whether each linear function is a direct variation. That was the directions. I don't understand how to find out whether each linear function is a direct variation. I'm thinking maybe you need to cross multiply? I don't know. Please help!

Celena Meng

BTW, can you explain just question 1? I just need to be able to understand the formula of doing this type of question.

 
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Re: Algebra Readiness Fall Question help
by Areteem Professor - Friday, October 25, 2019, 11:31 AM
 

When you have a table of values and want to see if it shows a direct variation you need to check if the ratios $\dfrac{y}{x}$ are equal each time.

For example in $$\begin{array}{|c|c|c|c|c|} \hline x & 2 & 4 & 6 & 8 \\ \hline y & 5 & 10 & 15 & 20 \\ \hline \end{array}$$ we can see the ratios $\dfrac{y}{x}$ are $$\dfrac{5}{2} = \dfrac{10}{4} = \dfrac{15}{6} = \dfrac{20}{8}.$$ Since all ratios are the same we can say the table shows a direct variation. If any of those ratios was not equal to the rest, then we would have said the table does not show a direct variation.

Remember, in general, we say $y$ varies directly with $x$ if there is some number $k$ (that does not change) such that you can always write $y = kx$.