Please help with the following problem:
Suppose that x and y vary directly, and x=4 when y=10. Write the function that models the direct variation.
y = kx
plug in the given values of x and y, then solve for k
rewrite the original equation, now that you know k
To write the function that models the direct variation, we need to find the constant of variation (k) first.
Direct variation can be represented by the formula: y = kx, where y represents the dependent variable, x represents the independent variable, and k represents the constant of variation.
Given that x and y vary directly, and x = 4 when y = 10, we can substitute these values into the formula:
10 = k * 4
To find the value of k, we divide both sides of the equation by 4:
10/4 = k
k = 2.5
Now that we have the value of k, we can write the function that models the direct variation:
y = 2.5x