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 195: 47


$y = -\frac{3}{2}x + 5$

Work Step by Step

We are given the line $3x + 2y = 10$. This equation is in standard form, which is given by the formula: $Ax + By = C$ However, we want this line in slope-intercept form. The first thing we want to do is isolate the $y$ term by moving the $x$ term to the other side of the equation. We do this by subtracting $3x$ from each side of the equation: $3x - 3x + 2y = -3x + 10$ Add to simplify the equation: $2y = -3x + 10$ To isolate $y$, we divide both sides by $2$: $\frac{2y}{2} = \frac{-3x}{2} + \frac{10}{2}$ Divide to simplify: $y = -\frac{3}{2}x + 5$ This line is now rewritten in slope-intercept form.
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