Solve for $y$.
$
\begin{array}{l}
y+2=5(x-3) \\
y=[?] x+\square
\end{array}
$
Answer (1)
Distribute the 5: y + 2 = 5 x − 15 .
Subtract 2 from both sides: y = 5 x − 17 .
Identify the coefficients: The equation is in the form y = [ ?] x + □ .
State the final answer: y = 5 x − 17
Explanation
Understanding the Problem We are given the equation y + 2 = 5 ( x − 3 ) and asked to solve for y and express the equation in the form y = [ ?] x + □ . This means we want to isolate y on one side of the equation and write the other side in the form of a linear expression m x + b , where m is the coefficient of x and b is a constant.
Distributing the 5 First, distribute the 5 on the right side of the equation:
y + 2 = 5 ( x − 3 )
y + 2 = 5 x − 15
Isolating y Next, subtract 2 from both sides of the equation to isolate y :
y + 2 − 2 = 5 x − 15 − 2
y = 5 x − 17
Final Answer The equation is now in the form y = [ ?] x + □ , where [ ?] = 5 and □ = − 17 . Therefore, the solution is y = 5 x − 17 .
Examples
Understanding linear equations like this is crucial in many real-world scenarios. For instance, imagine you're saving money. If you start with $2 and save $5 each week, the equation y = 5x - 17 can model your savings after x weeks, where y represents your total savings. This equation helps you predict how much money you'll have saved after a certain number of weeks, or how many weeks it will take to reach a specific savings goal. Linear equations are fundamental in financial planning, physics, and engineering, providing a way to model and predict outcomes based on constant rates of change.
