x and y vary directly. If y = 24 when x = 8, what is the variation constant and write the variation equation.
explain work
buttockss
To find the variation constant and write the variation equation, we need to use the given information that x and y vary directly.
When two variables vary directly, it means that they are related by a constant ratio. Mathematically, this can be represented as y = kx, where k is the variation constant.
Now, we are given that y = 24 when x = 8. We can substitute these values into the direct variation equation to find the value of k.
24 = k * 8
To find k, we can divide both sides of the equation by 8:
24/8 = k
3 = k
So, the variation constant, k, is 3.
Now, we can write the variation equation using the value of k:
y = 3x
Therefore, the variation constant is 3, and the variation equation is y = 3x.
if y varies directly with x, then there is a constant c such that
y = cx
so, plug in your x,y values to get c:
24 = c*8
3 = c
y = 3x