Solve for y.
$-11 x+y=6$
The problem requires solving the linear equation \(-11x + y = 6\) for the variable \(y\). We have a single equation involving two variables, \(x\) and \(y\). Our goal is to isolate \(y\) on one side of the equation to express it as a function of \(x\). To do this, we need to move the \(-11x\) term from the left side to the right side using the properties of equality.
To isolate \(y\), we perform the inverse operation of subtracting \(11x\), which is adding \(11x\) to both sides of the equation:
\[-11x + y + 11x = 6 + 11x\]
Simplifying the left side, \(-11x + 11x\) equals \(0\), leaving us with just \(y\). On the right side, we combine the constants and terms to get \(11x + 6\).
Thus, the equation becomes:
\[y = 11x + 6\]
Comparing our derived expression \(y = 11x + 6\) with the given options:
The derived expression matches the second option. Therefore, the solution is \(y = 11x + 6\).
In real-life scenarios, rearranging linear equations is essential in fields like physics or economics to express one variable in terms of another. For instance, if you are calculating the total cost of a service where a fixed fee is applied, or finding a position based on velocity and time, you often rearrange formulas such as \(y = mx + b\) to isolate variables, which helps in plotting data on a graph or predicting future outcomes based on changing parameters.