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?

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Answer 1 · 2016-03-21T20:03:37

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 $x$

$yxx x/x=9x$

$yxx1=9x =kx$