Solve the second equation for \(y\): \(y = 4x - 5\).

["Solve the Second Equation for (y): (y = 4x - 5)", "Mastering linear equations is essential for anyone studying algebra, and solving for one variable is a foundational skill. One commonly encountered equation is (y = 4x - 5), a simple linear expression that clearly defines (y) in terms of (x). In this article, we’ll dive into how to solve this equation for (y), why it matters, and how it fits into broader math concepts.", "---", "### Understanding the Given Equation", "The equation (y = 4x - 5) is already solved for (y), meaning (y) is explicitly expressed as a function of (x). The slope is 4, and the y-intercept is (-5), indicating that when (x = 0), (y = -5). This form—(y) directly in terms of (x)—is valuable because it allows quick evaluation of (y) for any given (x).", "---", "### Why Solve for (y)?", "Writing equations in the form (y = mx + b) (slope-intercept form) simplifies graphing, substitution, and real-world applications. When solving for (y), you prepare expressions to:", "- Plot points on a coordinate graph\n- Substitute (y) into other equations to solve systems\n- Model relationships in physics, economics, and engineering", "Though this equation is already solved, solving for (y) remains a core algebraic technique applicable even when equations aren’t initially in that form.", "---", "### How to Solve (y = 4x - 5) for (y)", "The solution is straightforward—there’s no complex manipulation required here:", "[\ny = 4x - 5\n]", "That expression defines (y) explicitly in terms of (x). For example:", "- If (x = 2), then (y = 4(2) - 5 = 8 - 5 = 3)\n- If (x = -1), then (y = 4(-1) - 5 = -4 - 5 = -9)", "But the beauty of (y = 4x - 5) lies in its direct relationship: for each input (x), the corresponding output (y) follows simply by multiplying (x) by 4 and subtracting 5.", "---", "### Practical Applications of the Equation", "Linear equations like (y = 4x - 5) model many real-world scenarios:", "- Cost calculations: If (x) is the number of items and each costs $4 (slope), plus a $5 service fee (y-intercept), then total cost (y = 4x - (-5)) becomes (y = 4x + 5), depending on context.\n- Distance-time relationships: If an object travels at 4 m/s and starts 5 meters from the origin, position (y) after (x) seconds is (y = 4x + 5).\n- Simple budgeting: Weekend spending with fixed costs and hourly rates often follows such forms.", "---", "### Key Takeaways", "- The equation (y = 4x - 5) is already solved for (y), introducing a standard linear form.\n- This structure supports graphing, substitution, and interpretation of real-world data.\n- Recognizing and manipulating linear equations in (y = mx + b) form builds confidence in exponential problem-solving across math and science disciplines.", "---", "### Conclusion", "Solving for (y) in (y = 4x - 5) is uncomplicated but foundational. It reinforces your understanding of linear functions and prepares you for solving more complex systems of equations. Whether for homework, standardized tests, or everyday calculations, mastering this expression gives you a reliable tool in algebra.", "Remember:\n[\n\boxed{y = 4x - 5}\n]\nis the direct solution—your key to plugging in values and analyzing relationships with confidence.", "---", "Need more practice? Try solving these:\n- (y = 2x + 7)\n- (y = -3x + 4)", "Use the same direct form—your algebra skills will grow with every equation solved!"]