Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 3 - Parallel and Perpendicular Lines - 3-7 Equations of Lines in the Coordinate Plane - Practice and Problem-Solving Exercises - Page 196: 64



Work Step by Step

We are given the two points, $(8, k)$ and $(7, -3)$. We are also given that the numerical value of the slope is $m = 5$. Let's use the formula to find the slope $m$ given two points: $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line. Let's plug in the values into this formula: $5 = \frac{-3 - k}{7 - 8}$ Subtract the numerator and denominator to simplify: $5 = \frac{-3 - k}{-1}$ Divide the numerator and denominator by their greatest common factor, which is $-1$: $5 = 3 + k$ To solve for $k$, we subtract $3$ from each side of the equation: $3 - 3 + k = 5 - 3$ Subtract to simplify: $k = 2$ This answer corresponds to option $B$.
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