Find the variation constant and an equation of variation where y varies directly as x and y = 20 when x = 10
To find the variation constant and an equation of variation where y varies directly as x, we can use the formula for direct variation:
y = kx
where y is the dependent variable, x is the independent variable, and k is the variation constant.
We are given that y = 20 when x = 10. We can substitute these values into the equation to solve for k.
20 = k * 10
Divide both sides of the equation by 10 to isolate the variation constant:
k = 20 / 10
Simplifying the right side gives:
k = 2
So, the variation constant is 2.
Now that we have the variation constant, we can write the equation of variation:
y = 2x
This equation represents direct variation, where y varies directly with x, and the variation constant is 2.