Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Review Exercises - Page 302: 56

Answer

The equation of the line passing through $\left( 1,\ 6 \right)$ and $\left( -1,\ 2 \right)$ in point-slope and slope-intercept form is $y-2x-4=0$ and $y=2x+4$ respectively.

Work Step by Step

Two points on the line are given as $\left( 1,\ 6 \right)$ and $\left( -1,\ 2 \right)$. Point-Slope form: It is known that the equation of the line by point-slope form will be: $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$ , Where $\begin{align} & m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & m=\frac{2-6}{-1-1} \\ & m=\frac{-4}{-2} \\ & m=2. \end{align}$ Now, substituting the given data in the above equation to get the desired equation of the line: $\begin{align} & y-2=2\left\{ x-\left( -1 \right) \right\} \\ & y-2=2\left( x+1 \right) \\ & y-2=2x+2 \\ & y-2x-4=0. \end{align}$ Slope-Intercept form: The above equation can be rewritten as: $y=2x+4$. Compare the above equation with the general equation of slope-intercept form: $\begin{align} & y=mx+c \\ & \text{Therefore,} \\ & m=2 \\ & c=4. \end{align}$ Therefore, the equation of the line passing through $\left( 1,\ 6 \right)$ and $\left( -1,\ 2 \right)$ in point-slope and slope-intercept form is $y-2x-4=0$ and $y=2x+4$ respectively.
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