If y varies directly with x, if y = 36 when x = -6, how do you find x when y = 54?

1 Answer
Jan 16, 2016

#x= -9#

Explanation:

Let #k# be a constant

Breaking down the question into parts:

If #y# varies directly with #x : -> y=kx........................(1)#
if #y=36 # when # x=-6->36=kxx(-6) ..........(2)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("To find the value of "k)#

Consider equation (1)

#color(brown)(y=kx)#

Divide both sides by #x#. This is the same as #color(blue)(xx1/x)#

#color(brown)(ycolor(blue)(xx1/x)=kxcolor(blue)(xx1/x))#

#y/x=kxx x/x#

But #x/x=1# giving:

#k=y/x ........................................(3)#

Substitute values from (2) into equation (3) giving

#color(blue)(k=36/(-6) =-6)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the value of "x" when "y=54)#

Using equation (1)

# y=kx-> 54=-6 x#

#color(blue)(=>x=54/(-6) = -9)#