Suppose that y varies inversely with x and that y = 4 when x = 6. What is an equation for the inverse variation?
A. y equals 6 divided by 4 times x.
B. y equals 24 divided by x.
C. y equals two-thirds times x.
D. y equals x divided by 24.
inversely means ... y * x = k
in this case , k = 24 ... y * x = 24
dividing by x ... y = 24 / x
Plz help
To find an equation for the inverse variation, we can use the inverse variation formula, which is y = k/x, where k is the constant of variation.
Given that y varies inversely with x and y = 4 when x = 6, we can substitute these values into the equation to find the constant of variation.
4 = k/6
To solve for k, we can multiply both sides of the equation by 6 to eliminate the fraction.
4 * 6 = k
24 = k
Now that we have the value of k, we can substitute it back into the inverse variation formula to find the equation.
y = 24/x
So, the equation for the inverse variation is y = 24/x.
Therefore, the correct answer is B. y equals 24 divided by x.
To determine the equation for inverse variation, we can start by stating the general equation for inverse variation as:
y = k/x, where k is the constant of variation.
Given that y varies inversely with x and that y = 4 when x = 6, we can substitute these values into the equation to solve for the constant of variation, k.
4 = k/6. To isolate k, multiply both sides of the equation by 6:
4 * 6 = k
24 = k
Now that we have the value of k, we can substitute it back into the general equation:
y = 24/x
Comparing this equation with the given answer choices:
A. y equals 6 divided by 4 times x. - This is not equivalent to the equation we determined.
B. y equals 24 divided by x. - This is equivalent to our equation, so it is a possible correct answer.
C. y equals two-thirds times x. - This is not equivalent to the equation we determined.
D. y equals x divided by 24. - This is not equivalent to the equation we determined.
Therefore, the correct equation for the inverse variation is:
B. y equals 24 divided by x.