Question

If y varies directly with x, how do you find y when x = 3, if y = -3, when x = 6?

Answer 1

Hint: We will assume that y = kx and then put in the given x = 3 and y = - 3 and get the value of k and put it in the assumed equation and then later on put x = 3, to get the value of y.

Complete step-by-step answer:
Since we are given that y varies directly with x. Therefore, y must be directly proportional to x.
We will assume that y = kx for some real value of k.
Now, we are also given that when x = 3, then y = - 3.
Putting x = 3 and y = - 3 in the equation we assumed that is y = kx.
We will then obtain the following equation:-
$ \Rightarrow $ - 3 = k (3)
If we multiply the right hand side, we will then get the following expression:-
$ \Rightarrow $ - 3 = 3k
On dividing the above equation by 3 on both the sides, we will then assume the following expression:-
$ \Rightarrow $ k = - 1
Hence, now we have k = - 1. Putting this in assumed equation which is y = kx, we get:-
$ \Rightarrow $ y = - x
Now, putting the value of x = 3 in above equation, we will then assume:-
$ \Rightarrow $ y = - 3

Thus, we have the required answer.

Note:
The students must note that we reached the final solution using the fact that y is directly proportional to the x. Now, we were also given the value of y on one value of x.
Here, we have 3 variables that are y, x and k. But, we were given information accordingly as well, so we were able to reach the required solution.
If we would have given that y is inversely proportional to x, then x would have been in the denominator with k as numerator.