Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 5 - Linear Functions - 5-3 Slope-Intercept Form - Got It? - Page 309: 1


The slope of this equation is $ -\frac{1}{2} $, and the y-intercept is $ \frac{2}{3} $. The graph would shift 3 units down the y axis if the intercept moved down 3 units. However, the graph would not stretch, shrink or flip.

Work Step by Step

The location of the slope and y-intercept is the same for all linear functions in slope intercept form. The coefficient tied to the variable ($ -\frac{1}{2} $ ) is always the slope and the constant $ (\frac{2}{3}) $ is the y-intercept. A shift in the y-intercept only changes the location of the graph, as the y-intercept simply states where the graph will cross the y-intercept. Thus a 3 unit shift downward will simply shift the entire graph 3 units down on the y-axis.
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