A. The number \( m \) represents the slope of the line and the number \( b \) represents the \( y \)-intercept. B. The number \( m \) represents the slope of the line and the number \( b \) represents the \( x \)-intercept. C. The number \( m \) represents the \( y \)-intercept and the number \( b \) represents the slope of the line. D. The number \( m \) represents the \( x \)-intercept and the number \( b \) represents the slope of the line. Add the opposite of the \( y \)-term to both sides. \( \left.\begin{array}{l}3 x-4 y=8 \\ 3 x=4 y+8 \\ \text { Subtract the constant term from both sides. } \\ 3 x+\end{array}\right]=4 y \)

If you're delving into the wonderful world of linear equations, there's a bit of history worth exploring! Linear equations date back to ancient civilizations, with Babylonians solving problems involving linear relationships as early as 2000 BC. They may not have used the \(y = mx + b\) format, but their calculations laid the groundwork for modern algebraic concepts! Now, turning to real-world applications, linear equations are everywhere! From budgeting your monthly expenses to determining the trajectory of a rocket, understanding slopes and intercepts helps you model and predict real-life scenarios. For instance, if you're planning a road trip, you can use linear equations to estimate how far you'll travel over time based on your speed!