Question - Equations of Lines and Points
Solution:
The task is to find the equations of lines that are:(a) Parallel to the given line(b) Perpendicular to the given lineBoth lines must pass through a given point. The point in this instance is (-7, -2), and the given line is x = 1.(a) A line parallel to x = 1 is also a vertical line, because x = 1 is vertical. All vertical lines have equations of the form x = c, where c is a constant. Since the line we're trying to find must pass through the point (-7, -2), the value of c must be -7. Therefore, the equation of the line parallel to x = 1 and passing through (-7, -2) is:x = -7(b) A line perpendicular to a vertical line is a horizontal line. All horizontal lines have equations of the form y = k, where k is a constant. Since the line we're trying to find must pass through the point (-7, -2), the value of k must be -2. Therefore, the equation of the line perpendicular to x = 1 and passing through (-7, -2) is:y = -2So the answers are:(a) x = -7(b) y = -2
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