Question

I am confused with this question: Find teh value of y for a given value of x, if y varies directly with x. If y = 6 when x = 2, what is y when x = 5?

Answer 1

"y varies directly with x" ---- y = kx, where k is a constant
given: when x = 2, y = 6
6 = 2k
k = 3

so your equation is : y = 3x
when x = 5 , y = ....

or
direct variations can be solved by simple ratios
6/2 = y/5
2y = 30
y = .... (same as above)

Answer 2

If y varies directly with x, then that means, whenever x increases by a certain amount, y proportionally increases by the same amount.

For example, if x is doubled, y gets doubled too.

So basically, when y=6, then x=2.
Putting x=5 means multiplying the original x with 2.5
Hence, the original y value is also multiplied by 2.5 to get the new one.
y = 2.5 * 6
= 15

Answer 3

Arora said:
"If y varies directly with x, then that means, whenever x increases by a certain amount, y proportionally increases <b>by the same amount.</b> "
not true

Your answer of 15, even though correct, has nothing to do with the question, I can get 15 in an infinite number of ways, for some reason you chose 2.5 * 6

the function is y = 3x , from where did you get 2.5 ?