The variables x and y vary directly. When x=12, y=9. Write an equation that relates the variables.
y = kx
9 = 12k, so k = 3/4
y = 3/4 x
To find the equation that relates the variables x and y when they vary directly, we can use the formula for direct variation, which is given by:
y = kx
where k is the constant of variation.
We are given that when x = 12, y = 9. We can plug these values into the equation to find the value of k:
9 = k * 12
To solve for k, we divide both sides of the equation by 12:
9/12 = k
Simplifying the fraction gives:
3/4 = k
Now that we know the value of k, we can substitute it back into the equation to find the final equation that relates x and y:
y = (3/4)x