Question

The variables \(x\) and \(y\) vary directly. Use the given values of the variables to write an equation that relates \(x\) and \(y .\) $$x=6.3, y=1.5$$

Short answer

The final equation of direct variation that relates \(x\) and \(y\) is \(y = 0.23809x\).

Step-by-step solution

Understanding Direct Variation

In direct variation, the variables \(x\) and \(y\) are related by a constant of variation, noted by \(k\), such that \(y=kx\). We need to find the value of \(k\) to write an equation that relates \(x\) and \(y\).

Calculate 'k', the Variation Constant

Given \(x=6.3\) and \(y=1.5\), we substitute these values into the formula \(y=kx\) to find \(k\). Solving for \(k\) gives \(k= \frac{y}{x} = \frac{1.5}{6.3}\).

Final Equation of Direct Variation

Calculate the value of \(k\) from the previous step and substitute it back into the equation \(y=kx\) to get the equation of direct variation relating \(x\) and \(y\).