Question #f7758

2 Answers
Dec 18, 2017

#y = 11.5#
We can know if something is a direct variation, if both the quantities increase or decrease simultaneously.

Explanation:

#y# varies directly with #x #

Direct variation means: When the value of # x #increases, the value of #y# also increases, and vice versa, i.e. the values of both the variables will increase or decrease simultaneously.

Writing with proportionality sign: #x prop y#

When the proportionality sign is replaced by equal- to sign, a proportionality constant is to be multiplied:

#x = a xxy# .... where #a# is proportionality constant.

Given : y=5 when x=160,

#=> x = a y #
OR
# y = x/a#

We will first calculate the value of proportionality constant from above equation:
#=> a= x/y#

#=> a =160/5 = 32#

Asked :what is #y# when #x=368# ?

#y = x/a = 368 / 32= 11.5#

We can see that as the value of #x# increased, the value of #y# also increased.
Hence we can know if something is a direct variation by observing the variation proportionality.

When the value of one variable decreases with increase in value of other (and vice versa), it is inverse variation. Ex: If the speed of a vehicle is more, the time taken to cover a certain distance is less. Here Speed and time are the variables which are inversely proportional.

Dec 18, 2017

#y=11.5#

Explanation:

#"the initial statement is "ypropx#

#"to convert to an equation multiply by k the constant"#
#"of variation"#

#rArry=kx#

#"to find k use the given condition"#

#y=5" when "x=160#

#y=kxrArrk=y/x=5/160=1/32#

#"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=x/32)color(white)(2/2)|)))#

#"when "x=368#

#y=368/32=11.5#