Solve for $y$.
$\begin{array}{r}
-8 x+y=9 \\
y=[?] x+
\end{array}$
Answer (1)
Add 8 x to both sides of the equation − 8 x + y = 9 .
Simplify the equation to isolate y .
The resulting equation is y = 8 x + 9 .
The solution for y is y = 8 x + 9 .
Explanation
Isolating y We are given the equation − 8 x + y = 9 and asked to solve for y . This means we want to isolate y on one side of the equation. To do this, we need to eliminate the term − 8 x from the left side of the equation. We can accomplish this by adding 8 x to both sides of the equation.
Solving for y Starting with the given equation: − 8 x + y = 9 Add 8 x to both sides: − 8 x + y + 8 x = 9 + 8 x Simplify: y = 8 x + 9
Final Answer The equation is now in the form y = m x + b , where m is the coefficient of x and b is the constant term. In this case, m = 8 and b = 9 . Therefore, the solution for y is: y = 8 x + 9
Examples
Understanding how to solve for a variable is crucial in many real-world scenarios. For example, imagine you are planning a road trip and need to determine the total cost based on the number of miles you drive. If the cost per mile is constant and you have a fixed budget, solving for the number of miles you can drive helps you plan your trip effectively. Similarly, in budgeting and finance, rearranging equations to solve for specific variables allows you to make informed decisions about spending and saving.
