If y varies directly with x and y = -4 when x = 12.5, how do you find y when x = 24?

Question

Julia Adams · Accepted Answer

#y=-7.68# A direct variation can be written as #y=kx#. Since we are given a matched #x# and #y# value, we can first compute for the constant of variation #k#. #y=kx# #(-4)=k(12.5)# #(1/12.5)(-4)=(1/cancel12.5)k(cancel12.5)# #-4/12.5=k# #color(blue)(k=-0.32)# Now that we know the constant of variation, we can now solve for the value of #y# when #x=24#. #y=color(blue)(k)x# #y=color(blue)((-0.32))x# #y=color(blue)((-0.32))(24)# #color(red)(y=-7.68)#

Jameson Allen · Answer

undefined To find $ y $ when $ x = 24 $, first, determine the constant of proportionality $ k $ using the given values. Then, use the formula for direct variation $ y = kx $ to find $ y $ when $ x = 24 $.

Given:
$ y = -4 $ when $ x = 12.5 $

First, find $ k $:
$ y = kx $
$ -4 = k \times 12.5 $
$ k = -4/12.5 = -0.32 $

Now, use $ k $ to find $ y $ when $ x = 24 $:
$ y = -0.32 \times 24 = -7.68 $

Therefore, when $ x = 24 $, $ y = -7.68 $.

Abigail Allen · Answer

undefined To find y when x = 24 in a direct variation equation, use the formula:

y = kx

where k is the constant of variation.

First, find the value of k using the given values:
y = -4 when x = 12.5

-4 = k * 12.5

Solve for k:
k = -4 / 12.5

Then, plug in the value of k and x = 24 into the equation to find y:
y = (-4 / 12.5) * 24

y ≈ -7.68