If y varies inversely as x, and y = 12 as x = 2, how do you find y for the x-value of 6?

Question

Hazel Anglin · Accepted Answer

undefined To find y for the x-value of 6, we can use the inverse variation equation. First, we need to determine the constant of variation, which is denoted as k. In this case, since y varies inversely as x, we have the equation y = k/x.

To find k, we can substitute the given values of y and x into the equation. When y = 12 and x = 2, we have 12 = k/2. Solving for k, we multiply both sides by 2, giving us k = 24.

Now that we have the value of k, we can use it to find y for the x-value of 6. Plugging in x = 6 into the inverse variation equation, we have y = 24/6. Simplifying, we find y = 4.

Therefore, when x = 6, y is equal to 4.

Ethan Adkins · Answer

#x=4# As #x# and #y# are inversely proportional, the equation can be represented as #x = k/y#. Substituting #x=2# and #y=12#, we get #2 = k/12# => # k = 12*2# => #k=24#. Equation can be represented as #x = 24/y#. So, when #y = 6#, we get #x = 24/6# => #x=4#

Eva Abramson · Answer

#y = 4#

Write as an inverse proportion first then make an equation by multiplying by k,

#yprop1/x " " rArr " " y = k/x " " k = x xx y#

Find the value of k.

#k = 2 xx 12 = 24#

#y = 24/x " "rArr " "y = 24/6#

#y = 4#

You can now find any value of y or x if you are given the x or the y value.