Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.3 Lines - F.3 Assess Your Understanding - Page 30: 38


$y = -\dfrac{1}{2}x$

Work Step by Step

The formula to find the slope of two given points on a line is: $m = \dfrac{y_2 - y_1}{x_2 - x_2}$, where $m$ is the slope and $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. Let's plug the coordinates of the points $(-2, 1)$ and $(0, 0)$ into the formula: $$m = \dfrac{0 - 1}{0 - (-2)}$$ Simplify numerator and denominator: $$m = \dfrac{-1}{2}$$ Let's plug the slope and one of the two points we are given into the point-slope form of an equation, which is given by the formula: $y - y_1 = m(x - x_1)$, where $m$ is the slope of the line and $(x_1, y_1)$ is a point on that line. Let's use the point $(0, 0)$ to plug into the formula: $y - 0 = -\dfrac{1}{2}(x - 0)$ Simplify both sides of the equation: $y = -\dfrac{1}{2}x$
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