If y varies directly with x, and y = 45 when x = 5, how do you write the direct linear variation equation and what is the constant?

Question

Abigail Allen · Accepted Answer

The constant is 9 so #y=kx ->y=9x#

Basically we are back to the good fashioned ratio problem.

Solving by 'not' using the short cut method. I have opted to do this to demonstrate what is really happening with the numbers.

Let # k# be a constant

Then #y/x=k/1#

So for #y/x->45/5 = k/1#

To find the value of #k# we need to find a way of changing the denominator of 5 into 1 without changing the intrinsic value of #45/5#

Maintaining the proportionality of this relation ship what I am about to do to the top (numerator) I will also do to the bottom (denominator)

Divide top and bottom by 5

#(45-:5)/(5-:5) = k/1" "# This is where the shortcut comes from.

#9/1=k/1 =>k=9# '~~~~~~~~~~~~~~~~~~~~~~~~~~ So the relation ship is

#y/x=45/5=9/1#

#y/x=9/1#

Multiply both sides by #x#

#yxx x/x=9x#

#yxx1=9x =kx#

Eva Adamson · Answer

undefined The direct linear variation equation is y = kx, where k is the constant of variation. Given that y = 45 when x = 5, we can solve for k: k = y / x = 45 / 5 = 9. Therefore, the direct linear variation equation is y = 9x, and the constant of variation is 9.