Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.2 - Mathematical Models: A Catalog of Essential Functions. - 1.2 Exercises - Page 34: 14


a) The graph is on the figure below. b) 1) The slope represents how much the number of spaces rented decrease when the price increases by $\$1$. 2) The $y$ intercept represents the number of spaces rented when they are free (the price $x=0$). 3) The $x$ intercept represents how much you have to charge so that you rent none of the spaces ($y=0$).

Work Step by Step

We will sketch this graph using that 1) for $y=0$: $$200-4x=0\Rightarrow 4x=200\Rightarrow x=50,$$ so it intercepts $x$ axis at $x=50$; 2) for $x=0$: $$y=200-4\times0=200$$ so it intercepts the $y$ axis at $y=200.$ Just connect those two points to get the graph but the line should not leave the first quadrant since both $x$ and $y$ are positive. This graph is shown on the figure below.
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