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Writing Equations of Perpendicular Lines

Writing Equations of Perpendicular Lines 1.5 - Solution

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a

Parallel lines have exactly the same slope. Therefore, to find the slope of a parallel line, we need to know the slope of the given line.

We can calculate it by substituting points that lie on the given line into the slope formula. Let's use and
Simplify right-hand side
The slope of the given line and, consequently, of the parallel line is Next, by substituting the slope and the given point, into the slope-intercept form, we can find the intercept of the desired line.
Solve for
We can now use the slope and intercept to write the equation of the parallel line in slope-intercept form.
b
We want to find the equation of a perpendicular line through the given point. When two lines are perpendicular, their slopes are negative reciprocals. This means that the product of their slopes must be From part A, we know that the slope of the given line is We can substitute this into the above equation to solve for the slope of the perpendicular line.
The slope of the perpendicular line is Once again, by substituting the slope and the given point, into the slope-intercept form, we can find the intercept.
Solve for
We can now use the slope and intercept to write the equation of the perpendicular line through