Given that y varies directly with x, how do you write a direct variation equation that relates x and y for x = 5, y = 10?

Answer 1

If #y# varies directly with #x#, then #y = mx# for some constant #m#

We are told that this relation holds for #(x,y) = (5,10)# so #10 = m*5# #rarr m = 2# and our direct variation equation is #y = 5x#

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Answer 2

Genesis Allen

The direct variation equation relating (x) and (y) for the given values (x = 5) and (y = 10) is:

[y = kx]

where (k) is the constant of variation. To find (k), we divide (y) by (x):

[k = \frac{y}{x} = \frac{10}{5} = 2]

Therefore, the direct variation equation is:

[y = 2x]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.