Solve for $y$.
$
\begin{array}{r}
2 y-2 x=4 \\
y=[?] x+
\end{array}$
Answer (1)
Add 2 x to both sides of the equation: 2 y = 2 x + 4 .
Divide both sides by 2 : y = x + 2 .
Express the equation in the desired form: y = 1 x + 2 .
The solution is y = x + 2 .
Explanation
Understanding the Problem We are given the equation 2 y − 2 x = 4 , 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 the y term First, we add 2 x to both sides of the equation to get rid of the − 2 x term on the left side: 2 y − 2 x + 2 x = 4 + 2 x 2 y = 2 x + 4
Solving for y Next, we divide both sides of the equation by 2 to solve for y :
2 2 y = 2 2 x + 4 y = 2 2 x + 2 4 y = x + 2
Final Answer Therefore, the equation is in the form y = 1 x + 2 .
Examples
In real life, this type of equation can be used to model a simple linear relationship between two variables. For example, if you are selling lemonade and you have a fixed cost of $4 (perhaps for the stand and initial supplies) and each cup of lemonade costs 1 t o mak e , t h e n t h e t o t a l cos t y t o mak e x c u p so f l e m o na d ec anb ere p rese n t e d b y t h ee q u a t i o n y = x + 4 . S o l v in g f or y in t er m so f x$ allows you to easily calculate the total cost for any number of cups of lemonade.
