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: 62


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

Work Step by Step

If two lines are parallel to one another, then they should have the same slope. First, let us find the slope of the line given. This line is written in standard form, so we want to rewrite this line in slope-intercept form, which is given by the following formula: $y = mx + b$, where $m$ is the slope of the line and $b$ is the $y$-intercept. We can rewrite our equation by isolating our $y$ term. First, we subtract $x$ from each side of the equation: $-2y = -x - 5$ Divide both sides of the equation by $-2$ to isolate $y$: $y = \dfrac{1}{2}x + \dfrac{2}{5}$ So the slope of this line is the coefficient of $x$; in this case, the slope of this line is $\dfrac{1}{2}$. Therefore, the slope of the line whose equation we want to find is also $\frac{1}{2}$. Let us plug this slope and the point we are given into the point-slope form of the 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 us use the point $(0, 0)$ to plug into the formula: $y - 0 = \dfrac{1}{2}(x - 0)$ Simplify the equation: $y = \dfrac{1}{2}x$ This equation is already in slope-intercept form, so we do not need to rewrite it any further.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.