Investigate this idea to develop a process for isolating a variable.
- Use the equation \(3x-2y=6\).
- Substitute the value \(x=4\) into the equation \(3x-2y=6\). Isolate the variable \(y\) by solving the equation for \(y\).
\[3x-2y=6\]
\[3(4)-2y=6\]
\[12-2y=6\]
\[12-12-2y=6-12\]
\[-2y=-6\]
\[\frac{-2y}{-2}=\frac{-6}{-2}\]
\[y=3\]
- Substitute the value \(x=-6\) into the equation \(3x-2y=6\). Isolate the variable \(y\) by solving the equation for \(y\).
\[3x-2y=6\]
\[3(-6)-2y=6\]
\[-18-2y=6\]
\[-18+18-2y=6+18\]
\[-2y=24\]
\[\frac{-2y}{-2}=\frac{24}{-2}\]
\[y=-12\]
- Now solve the equation \(3x-2y=6\) for \(y\) without knowing a value for \(x\). Leave your answer in terms of \(x\) which means that “\(x\)” will remain in your final equation.
\[3x-2y=6\]
\[3x-3x-2y=6-3x\]
\[-2y=-3x+6\]
\[\frac{-2y}{-2}=\frac{-3x+6}{-2}\]
\[y=\frac{3}{2}x-3\]
- What is the slope of the line \(3x-2y=6\)? The slope = \(\frac{3}{2}\)
- What is the \(y\)-intercept of the line \(3x-2y=6\)? The \(y\)-intercept is \((0,-3)\)
2. Solve the equation \(4x+2y=24\) for “\(y\)” in terms of “\(x\)” and identify the slope and the \(y\)-intercept.
\[4x+2y=24\]
\[4x-4x+2y=-4x+24\]
\[\frac{2y}{2}=\frac{-4x+24}{2}\]
\[y=-2x+12\]
- The slope = \(-2\)
- The \(y\)-intercept is \((0,12)\)
