Solve for $y$.
$
\begin{array}{l}
y+4=-2(x-5) \\
y=[?] x+\square
\end{array}
$
Answer (1)
Distribute − 2 on the right side: y + 4 = − 2 x + 10 .
Subtract 4 from both sides: y = − 2 x + 10 − 4 .
Simplify the equation: y = − 2 x + 6 .
The solution is y = − 2 x + 6 .
Explanation
Understanding the Problem We are given the equation y + 4 = − 2 ( x − 5 ) and we want to express it in the form y = [ ?] x + □ . Our goal is to isolate y and rewrite the equation in slope-intercept form ( y = m x + b ).
Distributing First, distribute the − 2 on the right side of the equation: y + 4 = − 2 ( x − 5 ) becomes y + 4 = − 2 x + 10 .
Isolating y Next, subtract 4 from both sides of the equation to isolate y : y = − 2 x + 10 − 4 .
Simplifying Finally, simplify the equation: y = − 2 x + 6 . The equation is now in the form y = [ ?] x + □ , where [ ?] = − 2 and □ = 6 .
Examples
Understanding linear equations is crucial in many real-world scenarios. For instance, if you are saving money, you can model your savings with a linear equation where the amount you save each week is the slope and your initial savings is the y-intercept. Similarly, in physics, the distance traveled at a constant speed can be modeled using a linear equation, where speed is the slope and initial distance is the y-intercept. This problem demonstrates how to manipulate and solve linear equations, which is a fundamental skill in various fields.
