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?
"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)
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
Arora said:
"If y varies directly with x, then that means, whenever x increases by a certain amount, y proportionally increases by the same amount. "
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 ?
To find the value of y when x = 5, given that y varies directly with x, we can use the formula for direct variation which is:
y = kx
In this formula, k represents the constant of variation.
To determine the value of k, we can use the given information that y = 6 when x = 2. By substituting these values into the formula, we have:
6 = k * 2
To solve for k, divide both sides of the equation by 2:
k = 6 / 2
k = 3
Now that we have the value of k, we can substitute it back into the original equation:
y = 3x
Finally, we substitute x = 5 into the equation to find the value of y:
y = 3 * 5
Evaluating this expression, we get:
y = 15
Therefore, when x = 5, y is equal to 15.