If y varies directly with x, if y=4 when x=16, how do you find y when x=6?

Question

Abigail Allen · Accepted Answer

A direct variation is always of the form #y=mx# The pair #(16,4)# gives us the constant #m# to be #1/4#, because #4=1/4 xx16# Now for any value of #x#, the value of #y=1/4x# #x=6->y=1/4xx6=6/4=1 1/2#

Genesis Allen · Answer

undefined To find $ y $ when $ x = 6 $, given that $ y $ varies directly with $ x $ and $ y = 4 $ when $ x = 16 $, you can use the direct variation formula.

The direct variation formula states: $ y = kx $, where $ k $ is the constant of variation.

First, find the constant of variation ($ k $) using the given values: $ y = 4 $ when $ x = 16 $.

$$ 4 = k \times 16 $$

$$ k = \frac{4}{16} = \frac{1}{4} $$

Now that you have the value of $ k $, you can use it to find $ y $ when $ x = 6 $:

$$ y = \frac{1}{4} \times 6 = \frac{6}{4} = 1.5 $$

So, when $ x = 6 $, $ y = 1.5 $.

Kennedy Adams · Answer

undefined To find the value of y when x equals 6 in a direct variation, you can use the direct variation formula. First, determine the constant of variation (k) by dividing y by x when they are given values. Then, use this constant to find y when x equals 6.

In this case, when y equals 4 and x equals 16, you can find the constant of variation (k) by dividing 4 by 16, which equals 0.25.

Then, using the constant of variation, you can find y when x equals 6 by multiplying 0.25 by 6, which equals 1.5.

Therefore, when x equals 6, y equals 1.5.