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Algebra Readiness Fall Question help
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 $y = kx$.
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