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: 83

Answer

The slope is undefined. The line does not have a $y$-intercept. See the graph below.

Work Step by Step

For a vertical line, its equation's form is always the following: $x=a$, where $a$ is a constant. Here, the equation $x=-4$ is exactly as described above with $a=-4$. Therefore the line is vertical. Recall that a vertical linehas an undefined slope, and that if the line itself is not the $y$-axis ($x=0)$, it has no $y$-intercept. The given line is not the $y$-axis, therefore it does not have a y-intercept. Every point that has an $x$-coordinate of $-4$ is on the line given in the exercise. Therefore, in order to sketch the line we only have to find two points with this attribute. For example, $(-4,0)$ and $(-4,1)$. Plot these poins then connect them using a straight line. Refer to the graph above.
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