I have no clue what to do here can you tell me how to figure this?
If y varies directly with x, and y = 500 when x = 200, find the constant of variation k.
Whenever you have a statement such as
"....y varies directly with x..."
you can write it as an equation y = kx, where k is some constant
so in your case they give you x=200, y=500
sub those values into the equation and you can solve for k
This is an example of a direct variation.
You can also have an "inverse variation", such as...
"The Time taken for a trip varies inversely with the speed"
then your equation would be Time = k(1/speed), again where k is some constant.
To solve for the constant of variation, k, when y varies directly with x, you can use the given values of x and y.
In this case, you are given that y = 500 when x = 200. You can substitute these values into the equation y = kx:
500 = k(200)
To solve for k, divide both sides of the equation by 200:
k = 500/200
Simplifying this expression gives you:
k = 2.5
So, the constant of variation, k, is 2.5.