The variables x and y vary directly. Use the values to find the constant of proportionality, k. Then write an equation that relates x and y. Write any fractions in simplest form.y=45; x=40

We are given that:
variables x and y vary directly, this means that:
y = kx where k is the constant of proportionality

Now, we are also given that:
y = 45 at x = 40.
We will use these values and substitute in the above relation to get k as follows:
y = kx
45 = 40k
k = 45/40 = 9/8 = 1.125

Based on the above calculations, the equation that relates x and y is:
y = 1.125x

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abidemiokin abidemiokin · Answer 2 · 2021-11-02T13:55:59+01:00

The constant of proportionality s 9/8 and the required equation that relates x and y will be [tex]y=\frac{9}{8}x[/tex]

If the variable x varies directly as the variable y, this is expressed using the equation below:

[tex]x \ \alpha \ y[/tex]

[tex]x = ky[/tex]

k is the constant of proportionality

Given that y = 45 and x = 40

Substitute the given parameters into the expression to have:

[tex]y = kx\\45 = 40k\\k=\frac{45}{40}\\k=\frac{9}{8}[/tex]

Hence the required equation that relates x and y will be [tex]y=\frac{9}{8}x[/tex]

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