Suppose y varies directly with x and y=12 when x=6. Write an equation realting x and y.
Please help, do not understand.
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when you have a statement such as
"Suppose y varies directly with x "
you can write it as y = kx, where k is some constant.
In most cases you will be given one relations that let's you find the value of k, sure enough: x=12 and x=6
so 12 = k(6)
k = 2
then your equation will be y = 2x
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thanks so much, very helpful
Well, we're dealing with a direct variation here, which means that y and x are related in a way that can be expressed as y = kx, where k is a constant.
To find the value of k, we can use the given information that y = 12 when x = 6. So, we substitute these values into the equation:
12 = k * 6
Now let's solve for k:
k = 12/6
k = 2
Now that we have the value of k, we can write the equation relating x and y:
y = 2x
So, the equation relating x and y is y = 2x. And keep in mind that in this scenario, I yamuseful and not yamusing!
To write an equation relating x and y in a direct variation, we need to find the constant of variation, which is the ratio between y and x. In this case, y varies directly with x, so we can express the relationship as:
y = kx
Where k is the constant of variation.
Given that y = 12 when x = 6, we can substitute these values into the equation:
12 = k * 6
To find the value of k, we can solve the equation for k:
k = 12 / 6
k = 2
Now that we have the value of k, we can substitute it back into the equation to obtain the final equation relating x and y:
y = 2x