Question

If y is directly proportional to x, then ___________

Answer 1

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If y is directly proportional to x, this means x is also directly proportional to y. so if y=kx then we can sayx=k'y, where k'=1/k.

y is directly proportional to x.

If y equals 30 when x is equal to 6,

find the value of x when y is 45.

So let's just take this each statement at a time.

y is directly proportional to x.

That's literally just saying that y is equal to some constant times x.

This statement can literally be translated to y is equal to some constant times x.

y is directly proportional to x.

Now, they tell us, if y is 30 when x is 6-- and we have this constant of proportionality-- this second statement right over here allows us to solve for this constant.

When x is 6, they tell us y is 30 so we can figure out what this constant is.

We can divide both sides by 6 and we get this left-hand side is 5-- 30 divided by 6 is 5.

5 is equal to k or k is equal to 5.

So the second sentence tells us, this gives us the information that y is not just k times x, it tells us that y is equal to 5 times x.

y is 30 when x is 6.

And then finally, they say, find the value of x when y is 45.

So when y is 45 is equal to-- so we're just putting in 45 for y-- 45 is equal to 5x.

Divide both sides by 5 to solve for x.

We get 45 over 5 is 9, and 5x divided by 5 is just x.

So x is equal to 9 when y is 45.