Question #fea28

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Question #fea28

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Answer 1 · 2017-04-20T16:38:54

$y - 5 = 2 x$ $y-5=2x$ is not an example of direct variation.

Explanation:

Direct variation means that one variable is equal to a constant times another variable. That is, $y = k x$ $y=kx$ . Rearranging the equation above, we get $y = 2 x + 5$ $y=2x+5$ which is obviously not in the form $y = k x$ $y=kx$ , but it can be proven a bit more convincingly that this is not direct variation by noting that whenever one variable varies directly as another, when one is zero so is the other. That is, if $y = k x$ $y=kx$ then when $x = 0$ $x=0$ , $y = 0$ $y=0$ . This is intuitively true because any $k$ $k$ times $0$ $0$ will be $0$ $0$ . Plugging $x = 0$ $x=0$ and $y = 0$ $y=0$ into the equation above we get a contradiction, thus when $x = 0$ $x=0$ , $y \neq 0$ $y!=0$ so the equation is not direct variation.
$(0) - 5 = 2 (0)$ $(0)-5=2(0)$
$- 5 = 0$ $"-"5=0$
$false$ $"false"$

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