The variables x=2 and y=7 varies directly. How do you write an equation that relates the variables and find y when x=8?

2 Answers
Nov 29, 2017

#y=28#

Explanation:

“The variables #x=2# and #y=7# vary directly.”

We can express that as:

#y=mx#

#\rightarrow 7=m\cdot 5#, where #m# is the constant of variation (slope).

Now, we need to solve for #m#:

#7=2m#

Divide both sides by #2#:

#m=\frac{7}{2}#

Now, we can plug this value, as well #x=8#, into the next equation to find #y#:

#y=mx#

#\rightarrow y=\frac{7}{2}\cdot 8#

#\rightarrow y=\frac{56}{2}#

#\rightarrow y=28#

Nov 29, 2017

#y =7/2x#
#y(8)=28#

Explanation:

I assume you mean that #x and y# vary directly and #x=2# when #y=7#

If so, then we know that:

#y = kx# for some constant #k#

Since #x=2# when #y=7#

#:. 7 = kxx2#

#->k=7/2#

Hence, #y =7/2x# is our required equation.

We are asked to find #y# when #x=8#

#-> y(8)=7/2xx8 = 7xx4#

#y(8)=28#