Question

If y is directly proportional to x and y = 5 when x =2, what is the value of y when x=6

Answer 1

y = 15

Explanation:

If the variables are directly proportional, increasing one by a factor of 3 will mean the other one also increases by a factor of 3.

6 is 3 times 2, so the value of y will be 3 times 5, or 15.

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You can write the relation as a proportion:

y/x = 5/2 = ?/6

Multiplying by 6 gives ...

(5/2)·6 = ? = 15

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Or, you can bother with an equation relating x and y:

y = kx

5 = k·2 . . . plug in the given values and solve for k

5/2 = k . . . divide by 2

Then ...

y = (5/2)·6 = 15 . . . . same as the proportion, above.

If you rearrange this to y = 5·(6/2) then you see the relation described at the beginning of this solution. The new value of y is the old value multiplied by the factor by which x changes.

Answer 2

y=15

Explanation:

The formula for direct variation is

y = kx

5 =k*2

Solve for k

Divide by 2

5/2 = k

y = 5/2 x

Now we substitute x=6

y = 5/2(6)

y = 15