Solve for $y$.
$
\begin{array}{l}
y+5 x=10 \\
y=[?] x+
\end{array}$
Answer (1)
Subtract 5 x from both sides of the equation y + 5 x = 10 .
Simplify the equation to isolate y .
The solution is y = − 5 x + 10 .
Therefore, the final answer is y = − 5 x + 10 .
Explanation
Understanding the Problem We are given the equation y + 5 x = 10 and we want to solve for y in terms of x . This means we want to isolate y on one side of the equation.
Isolating y To isolate y , we subtract 5 x from both sides of the equation: y + 5 x − 5 x = 10 − 5 x y = 10 − 5 x y = − 5 x + 10
Final Answer Therefore, y = − 5 x + 10 .
Examples
In physics, this type of equation can represent the motion of an object. For example, if y represents the position of an object at time x , the equation y = − 5 x + 10 tells us that the object starts at position 10 and moves backwards (since the coefficient of x is negative) at a rate of 5 units per unit of time. Understanding how to rearrange such equations allows us to predict the object's position at any given time.
