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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 An entomologist is studying the trajectory of a butterfly modeled as a line passing through \( (2, -3) \) and \( (5, 6) \). Determine the \(y\)-intercept of this line.

📌 First, compute the slope \(m\) of the line through points \((x_1, y_1) = (2, -3)\) and \((x_2, y_2) = (5, 6)\):

📌 \[ m = \frac{6 - (-3)}{5 - 2} = \frac{9}{3} = 3 \]

📌 Using point-slope form with point \((2, -3)\):

📌 \[ y - (-3) = 3(x - 2) \]

📌 \[ y + 3 = 3x - 6 \]

📌 \[ y = 3x - 9 \]

📌 The \(y\)-intercept occurs when \(x = 0\):

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