How do I set up this equation?
If Y varies directly as X and Y = 12 when X = 3, find Y when X = 16
If y varies directly with x, then there must be some number "k" such as:
y=k*x
Y = 12 when X = 3...So?
12=k*3
k=12/3
k=4
Since you found k, then you can plug in to find Y.
Y= 4*16
Y= 64
To set up the equation, you need to understand how variables Y and X are related.
When Y varies directly as X, it means that as X increases or decreases, Y will also increase or decrease by the same factor. This relationship can be expressed using the formula:
Y = kX
where "k" is the constant of variation.
To find the value of "k," we can use the given information that Y = 12 when X = 3. Plugging these values into the equation, we have:
12 = k * 3
To solve for "k," divide both sides of the equation by 3:
k = 12/3
k = 4
Now that we have the constant of variation, we can use it to find Y when X = 16.
Substitute the known values into the equation:
Y = kX
Y = 4 * 16
Y = 64
Therefore, when X = 16, Y will be equal to 64.