Suppose that y varies directly with x and inversely with z, and that y = 18 when x = 15 and z = 5. Write the equation that models the relationship. Then find y when x = 21 and z = 7. (1 point) Responses y = ; y = Image with alt text: five z over x ; Image with alt text: five-thirds y = ; 15 y = Image with alt text: five x over z ; 15 y = ; 18 y = Image with alt text: six x over z ; 18 y = ; 2
The correct equation that models the relationship is y = kx/z, where k is the constant of proportionality.
To find the value of k, we can plug in the values of y, x, and z given in the problem:
18 = k * 15/5
18 = 3k
k = 6
Now that we have the value of k, we can use it to find y when x = 21 and z = 7:
y = 6 * 21 / 7
y = 126 / 7
y = 18
Therefore, when x = 21 and z = 7, y = 18.