Question

When \(x=4, y=6 .\) For the given type of variation, find an equation that relates \(x\) and \(y .\) Then find the value of \(y\) when \(x=8\). \(x\) and \(y\) vary directly.

Short answer

The equation that relates \(x\) and \(y\) is \(y=1.5x\). The value of \(y\) when \(x=8\) is \(y=12\)

Step-by-step solution

Determine the Constant of Variation

In direct variation, the constant of variation \(k\) is given by \(k=\frac{y}{x}\). Here, for \(x=4\) and \(y=6\), we calculate \(k=\frac{6}{4}=1.5\)

Formulate the Equation of Variation

Substitute the calculated value of \(k\) into the formula for direct variation \(y=kx\). This gives us the equation \(y=1.5x\)

Find the Value of y when x=8

Substitute \(x=8\) into the formulated equation \(y=1.5x\). This gives us \(y=1.5*8=12\)