Solve for $y$.
$
\begin{array}{l}
y+4=-2(x-5) \\
y=[?] x+\square
\end{array}
$
Answer (1)
Distribute the -2 on the right side of the equation: y + 4 = − 2 x + 10 .
Subtract 4 from both sides to isolate y: y = − 2 x + 6 .
Identify the coefficient of x and the constant term.
The solution is y = − 2 x + 6 .
Explanation
Understanding the Problem We are given the equation y + 4 = − 2 ( x − 5 ) and we want to solve for y and express it in the form y = [ ?] x + □ . This means we need to isolate y on one side of the equation and simplify the other side.
Distributing -2 First, distribute the − 2 on the right side of the equation:
y + 4 = − 2 ( x − 5 ) y + 4 = − 2 x + 10
Isolating y Next, subtract 4 from both sides of the equation to isolate y :
y + 4 − 4 = − 2 x + 10 − 4 y = − 2 x + 6
Final Answer The equation is now in the form y = [ ?] x + □ . We can see that the coefficient of x is − 2 and the constant term is 6 . Therefore, the solution is y = − 2 x + 6 .
Examples
Understanding linear equations like this helps in various real-life scenarios. For example, if you are saving money and you start with $4 and save $2 every week, the equation y = 2x + 4 represents your total savings (y) after x weeks. Similarly, if you are losing weight, and the equation is y = -2x + 10, it means you started at 10 kg and lose 2 kg every week (x).
