Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.3 Lines - F.3 Assess Your Understanding - Page 31: 86

Answer

The slope is undefined. The line has no $y$-intercept. See the graph below.

Work Step by Step

For a vertical line, its equation's form is always $x=a$, where $a$ is a constant. Here, the equation $x=2$ is exactly as described above with $a=2$. Therefore the line is vertical. Recall that the slope of a vertical line is undefined. If the line itself is not the $y$-axis (which is $x=0$), it does not have a $y$-intercept. The line $x=2$ is not the $y$-axis, therefore it does not have a $y$-intercept. Every point that has an $x$-coordinate of $2$ is on the line $x=2$. Therefore, in order to sketch the line we can use the poiints $(2,0)$ and $(2,1)$. Plot the points then connect them using a straight line. Refer to the graph above.
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