5Question: An archaeologist measures the altitude of a Mayan pyramid's slope at different points, modeled by the equation $ y = -\frac{3}{5}x + b $. If the slope passes through the point $ (10, 2) $, find the $ y $-intercept $ b $.
["Understanding the Mayan Pyramid’s Slope: Solving for the y-Intercept in an Archaeologic Context", "When analyzing the architectural precision of ancient Mayan pyramids, archaeologists often rely on geometric modeling to reconstruct their design. One such analysis involves determining the equation of a pyramid’s slope, expressed as $ y = -\frac{3}{5}x + b $, where $ y $ represents height and $ x $ represents horizontal distance from a reference point.", "In this study, a key measurement confirms the slope passes through the point $ (10, 2) $. This real-world data allows researchers to solve for the $ y $-intercept $ b $, essential for understanding the pyramid’s original height at its base alignment.", "---", "### Step 1: Plug known values into the equation\nThe given slope equation is:\n[\ny = -\frac{3}{5}x + b\n]\nSubstitute $ x = 10 $ and $ y = 2 $:\n[\n2 = -\frac{3}{5}(10) + b\n]", "---", "### Step 2: Simplify the expression\nCalculate $ -\frac{3}{5} \ imes 10 $:\n[\n-\frac{3}{5} \cdot 10 = -6\n]\nNow substitute back:\n[\n2 = -6 + b\n]", "---", "### Step 3: Solve for $ b $\nAdd 6 to both sides:\n[\nb = 2 + 6 = 8\n]", "---", "### Conclusion: The y-intercept reveals architectural insight\nThe $ y $-intercept $ b = 8 $ represents the modeled height of the pyramid’s slope at $ x = 0 $, providing valuable data on the structure’s vertical rise relative to its base extent. This analytical approach bridges archaeology and mathematics, revealing how precise measurements shape our understanding of ancient engineering.", "For researchers studying Mayan pyramids, equations like $ y = -\frac{3}{5}x + 8 $ are not just abstractions—they connect physical remnants with the original grandeur of Mesoamerican architecture.", "---", "Keywords: Mayan pyramid, slope equation, y-intercept, archaeologist measurement, algebraic modeling, cultural heritage math, pyramid geometry, y-intercept Mayan pyramid, equation archaeology, ancient architecture analysis."]
