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Chapter 1: Problem 77

Write equations of the lines through the given point (a) parallel to and (b) perpendicular to the given line. $$y+3=0, \quad(-1,0)$$

Short Answer

Expert verified
The equation of the line parallel to the given line and passing through the point \(-1,0\) is \(y = 0\) and the equation of the line perpendicular to the given line and passing through the point \(-1,0\) is \(x = -1\).\n

Step by step solution

01

Find the Equation of the Line Parallel to the Given Line

The slope of the given line is \(0\), so the gradient of the line parallel to the given line will also be \(0\). Thus, the equation of the line parallel to the given line and passing through \(-1,0\) will have the form \(y = 0x + b\), and by substituting the point \(-1,0\) into the equation it gives \(0 = 0 * -1 + b\), thus the equation becomes \(y = 0\).
02

Find the Equation of the Line Perpendicular to the Given Line

For a line to be perpendicular to the given line, its slope should be the negative reciprocal of the slope of the given line. Since the slope of the given line is \(0\), the negative reciprocal will be undefined, which means the line is vertical at x = -1. Hence, the equation of the line perpendicular to the given one and passing through \(-1,0\) will be \(x = -1\).

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