$\begin{array}{r}3 x+y=3 \ y=[?] x+\end{array}$
Answer (1)
Start with the given equation: 3 x + y = 3 .
Isolate y by subtracting 3 x from both sides: y = − 3 x + 3 .
Identify the coefficient of x and the constant term.
The equation in the desired form is y = − 3 x + 3 .
Explanation
Understanding the Problem We are given the equation 3 x + y = 3 and we want to rewrite it in the form y = [ ?] x + [ ?] . This involves isolating y on one side of the equation.
Isolating y To isolate y , we subtract 3 x from both sides of the equation: 3 x + y − 3 x = 3 − 3 x y = − 3 x + 3
Identifying the Coefficients Now we can see that the equation is in the form y = [ ?] x + [ ?] , where the coefficient of x is − 3 and the constant term is 3 . Therefore, the equation is y = − 3 x + 3 .
Examples
Understanding how to rewrite equations in different forms is crucial in many real-world scenarios. For example, if you are tracking your expenses and know that your total spending is related to the number of items you buy, you can express this relationship as an equation. By rearranging the equation, you can easily determine how many items you can afford given a certain budget. This skill is also fundamental in physics, engineering, and economics, where equations are used to model and solve problems.
