Writing Equations of Parallel and Perpendicular Lines to Horizontal and Vertical Lines
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A horizontal line has the form [latex]y = c[/latex]
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A vertical line has the form [latex]x = c[/latex]
Parallel to Horizontal or Vertical Lines
(b) Write the equation of a line parallel to [latex]x = –5[/latex] that passes through the point [latex](2, 1)[/latex].
Perpendicular to Horizontal or Vertical Lines
It passes through [latex]x = –1[/latex], so the equation is:
[latex]x = –1[/latex](b) Write the equation of a line perpendicular to [latex]x = –2[/latex] that passes through the point [latex](–2, 3)[/latex].Since [latex]x = –2[/latex] is vertical, the perpendicular line must be horizontal.
It passes through [latex]y = 3[/latex], so the equation is:
[latex]y = 3[/latex]
Writing equations of lines parallel or perpendicular to horizontal and vertical lines:
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A line parallel to [latex]y = c[/latex] is another horizontal line: [latex]y = d[/latex]
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A line parallel to [latex]x = c[/latex] is another vertical line: [latex]x = d[/latex]
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A line perpendicular to [latex]y = c[/latex] is a vertical line: [latex]x = d[/latex]
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A line perpendicular to [latex]x = c[/latex] is a horizontal line: [latex]y = d[/latex]
Use the point given to find the value of [latex]x[/latex] or [latex]y[/latex].