Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.2 - Linear Models and Rates of Change - Exercises: 11

Answer

The graph of the lines is shown below:
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Work Step by Step

Point $(3,4)$ $a)$ $m=1$ Using the point-slope form of the equation of a line, the equation of this line is: $y-y_{0}=m(x-x_{0})$ $y-4=(1)(x-3)$ $y-4=x-3$ $y=x-3+4$ $y=x+1$ $b)$ $m=-2$ Using the point-slope form of the equation of a line, the equation of this line is: $y-y_{0}=m(x-x_{0})$ $y-4=(-2)(x-3)$ $y-4=-2x+6$ $y=-2x+6+4$ $y=-2x+10$ $c)$ $m=-\dfrac{3}{2}$ $y-y_{0}=m(x-x_{0})$ $y-4=-\dfrac{3}{2}(x-3)$ $y-4=-\dfrac{3}{2}x+\dfrac{9}{2}$ $y=-\dfrac{3}{2}x+\dfrac{9}{2}+4$ $y=-\dfrac{3}{2}x+\dfrac{17}{2}$ $d)$ Slope undefined If the slope is undefined, the line is a vertical line with $x$-coordinate equal to $3$ The equation of the line is: $x=3$
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