Solve for $y$. $\begin{array}{l} y+5=-2(x-1) \ y=[?] x+\square \end{array} $

Distribute the -2 on the right side of the equation: y + 5 = − 2 x + 2 .
Subtract 5 from both sides to isolate y: y = − 2 x + 2 − 5 .
Simplify the equation: y = − 2 x − 3 .
The solution is y = − 2 x − 3 , so the missing values are y = − 2 x − 3 ​ .

Explanation

Understanding the Problem We are given the equation y + 5 = − 2 ( x − 1 ) and asked to solve for y and express it in the form y = [ ?] x + □ .

Distributing the -2 First, we need to distribute the − 2 on the right side of the equation: y + 5 = − 2 ( x − 1 ) y + 5 = − 2 x + 2

Isolating y Next, we subtract 5 from both sides of the equation to isolate y :
y + 5 − 5 = − 2 x + 2 − 5 y = − 2 x + 2 − 5

Simplifying the Equation Now, we simplify the equation: y = − 2 x − 3

Finding the Solution The equation is now in the form y = [ ?] x + □ , where [ ?] = − 2 and □ = − 3 .
So the solution is y = − 2 x − 3 .


Examples
Understanding linear equations like this is crucial in many real-world scenarios. For instance, if you're tracking the depreciation of an asset over time, the equation can model how the value decreases linearly. If a car's initial value is $5000 and it depreciates $500 each year, the equation would be Value = -500*years + 5000. Solving such equations helps in financial planning and understanding rates of change.

Answered by GinnyAnswer | 2025-07-08

To solve for y in the equation y + 5 = − 2 ( x − 1 ) , we distribute the -2, isolate y , and simplify to find y = − 2 x − 3 . The coefficients are [ ?] = − 2 and □ = − 3 .
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Answered by Anonymous | 2025-07-11