Solve for y.
[tex]
\begin{array}{l}
y-4=2(x+5) \\
y=[?] x+\square
\end{array}
[/tex]
Answer (1)
The solution for y is y = 2 x + 14 .
Explanation
Understanding the Problem We are given the equation y − 4 = 2 ( x + 5 ) and asked to solve for y and express the equation in the form y = [ ?] x + □ , which is the slope-intercept form of a linear equation.
Distributing the Constant First, we distribute the 2 on the right side of the equation:
y − 4 = 2 ( x + 5 )
y − 4 = 2 x + 10
Isolating y Next, we isolate y by adding 4 to both sides of the equation:
y − 4 + 4 = 2 x + 10 + 4
y = 2 x + 14
Final Answer The equation is now in the form y = 2 x + 14 , where the coefficient of x is 2 and the constant term is 14. Therefore, the solution is y = 2 x + 14 .
Examples
Understanding linear equations is crucial in many real-world scenarios. For example, imagine you are saving money. If you start with $4 and save $2 every week, the equation y = 2x + 4 models your total savings (y) after x weeks. This equation helps you predict how much money you'll have saved after a certain number of weeks, which is a practical application of solving for y in a linear equation.
