Question

the value of y is directly proportional to the value of x. if y = 45 when x = 180 what is the value of y = 90

Answer 1

We have a direct proportionality between y and x.

If "k" is the constant of proportionality, the equation for this situation is:

`y=kx`

To find the constant of proportionality, we solve that equation for k:

`k=(y)/(x)`

And since when y=45, x=180, substituting these values to find k:

`\begin{gathered} k=(45)/(180) \\ k=0.25 \end{gathered}`

Now, we substitute the value of k into the equation of proportionality:

`y=0.25x`

And in this equation, we can substitute any value of the variables, and find the value of the other variable.

In this case, we have y=90, so we substitute that value and solve for x:

`\begin{gathered} 90=0.25x \\ (90)/(0.25)=x \\ 360=x \end{gathered}`

Answer: when y=90, x=360