Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.5 Equations of Lines and Linear Models - 2.5 Exercises: 24

Answer

$x=2$

Work Step by Step

RECALL: (1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line. (2) The slope $m$ of a line that contains the points $(x_1, y_2)$ and $(x_2, y_2)$ is given by the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$. (3) A vertical line has an equation of the form $x=h$. Every point on the line has an x-coordinate of $h$. The line is vertical so its equation is of the form $x=h$. The line contains the point $(2, 7)$, the x-coordinate of which is $2$. Therefore, the equation of the vertical line is $x=2$. This equation cannot be written in point-slope form.
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