Question

Rewrite the equation so that \(x\) is a function of \(y .\) Then use the result to find \(x\) when \(y=-2,-1,0,\) and 1. $$3 y-x=12$$

Short answer

The function is \(x = 3y - 12\). When \(y = -2\), \(x = -18\). When \(y = -1\), \(x = -15\). When \(y = 0\), \(x = -12\). When \(y = 1\), \(x = -9\).

Step-by-step solution

Rearrange the equation to make \(x\) the subject

In the equation \(3y - x = 12\), to isolate \(x\), we add \(x\) to both sides, and subtract \(12\) from both sides, resulting in \(x = 3y - 12\). This gives the function of \(x\) in terms of \(y\).

Substitute \(y = -2\) into the equation

Using the function \(x = 3y - 12\), substitute \(-2\) for \(y\). This results in \(x = 3(-2) - 12 = -6 - 12 = -18\). So when \(y = -2\), \(x = -18\).

Substitute \(y = -1\) into the equation

Substitute \(-1\) for \(y\) in the function \(x = 3y - 12\). This gives \(x = 3(-1) - 12 = -3 - 12 = -15\). So when \(y = -1\), \(x = -15\).

Substitute \(y = 0\) into the equation

Substitute \(0\) for \(y\) in the function \(x = 3y - 12\). This gives \(x = 3(0) - 12 = 0 - 12 = -12\). So when \(y = 0\), \(x = -12\).

Substitute \(y = 1\) into the equation

Substitute \(1\) for \(y\) in the function \(x = 3y - 12\). This gives \(x = 3(1) - 12 = 3 - 12 = -9\). So when \(y = 1\), \(x = -9\).