If y varies directly as x, and y = 30 when x = 4, how do you find the constant of proportionality?

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Answer 1 · 2016-05-31T19:13:42

It is $7.5$ $7.5$ .

if it varies directly means that $y$ $y$ is equal $x$ $x$ multiplied by something. I call this "something" $A$ $A$ .
So I write

$y = A x$ $y=Ax$

To find the value of $A$ $A$ I have to divide on both sides for $x$ $x$ obtaining

$\frac{y}{x} = A \frac{x}{x}$ $y/x=Ax/x$

the two $x$ $x$ on the right cancel each other and I remain with

$\frac{y}{x} = A$ $y/x=A$ .

Now I can substitute the numbers

$\frac{30}{4} = A$ $30/4=A$
$7.5 = A$ $7.5=A$ .

Then the proportionality constant is $7.5$ $7.5$ .