The value of #y# varies directly with #x#, and #y = -6# when #x = 3#. What is #y# when #x =12#?

Question

Julia Adams · Accepted Answer

#y = -24#

When anything varies directly with something else, it always indicated multiplication. So in this case, #y# varies directly with #x#. This can be written as:

#y = kx# (all direct variations take this original standard form)

We are also given that #y = - 6# when #x = 3#. What we can do with this information is fairly simple. Just plug in these values into the given formula/equation above.

#y = kx# #-6 = k(3)#

We are also asked to find #y# when #x# is #12#. We can't solve an equation like this without finding #k#. So let's solve for #k# form the equation we created above first.

#-6 = k(3)# #-2 = k#

Now that we know #k# is equal to #-2#, we can find what the question is asking.

#y = -2x# #y = -2(12)# #y = -24#

For a summary of what we accomplished here:

Avery Alexander · Answer

undefined Since the value of $ y $ varies directly with $ x $, we can set up a proportion to find $ y $ when $ x = 12 $. The given information is that $ y = -6 $ when $ x = 3 $.

Using the direct variation formula $ y = kx $, where $ k $ is the constant of variation, we can find $ k $ using the given values:

$$ -6 = k \cdot 3 $$

Solving for $ k $, we get $ k = -2 $.

Now that we have the constant of variation, we can use it to find $ y $ when $ x = 12 $:

$$ y = -2 \cdot 12 = -24 $$

Therefore, when $ x = 12 $, $ y = -24 $.