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: 83

Answer

$y=-5x-6$

Work Step by Step

Let $(-2,4)=(x_{1}, y_{1})$ and $(0,-6)=(x_{2}, y_{2})$ 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: $\frac{(-6)-(4)}{0)-(-2)}$ $=\frac{-10}{2}=-5$ The equation for a line is given by: $y-y_{1}=m\times(x-x_{1})$ Substituting $m=-5$ and $(x_{1}, y_{1})=(0,-6)$ $y-(-6)=-5(x-0)$ The expression can then be simplified to $y+6=-5x$ Subtracting $6$ from both sides, the solution $y=-5x-6$ is obtained.
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