Calculus 10th Edition

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

Chapter P - P.3 - Functions and Their Graphs - Exercises - Page 29: 84


$y=\frac{7}{2} x-\frac{19}{2}$

Work Step by Step

Let $(3,1)=(x_{1},y_{1})$ and $(5,8)=(x_{2},y_{2})$ The gradient of a line is given by the equation: gradient$=\frac{y_{2}-,y_{1}}{x_{2}-x_{1}}$ By substituting in the given points, the gradient, $m$, of the line is: $\frac{8-1}{5-3}$ $=\frac{7}{2}$ The equation for a line is given by: $y-y_{1}=m\times(x-x_{1})$ Substituting $m=\frac{7}{2}$ and $(3,1)=(x_{1},y_{1})$ $y-1=\frac{7}{2}( x-3)$ $y-1=\frac{7}{2} x-\frac{21}{2}$ Adding $1$ to both sides, $y=\frac{7}{2} x-\frac{19}{2}$
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