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Standard Form Page 2

Algebra 1 Notes SOL A.6 Standard Form;  and  Lines

Mrs. Grieser Page 2

Writing Equations of Parallel and Perpendicular Lines

Parallel Lines

Parallel lines have the same ______________;

Therefore two linear equations that have the same ____________ are parallel.

Example: Write an equation of a line that passes through point (-3, -5) and is parallel to

the line y = 3x – 1.

Step 1: Slope = __________

Step 2: Use point-slope to find the equation ____________________________________

Perpendicular Lines

 If two nonvertical lines in the same plane have slopes that are negative reciprocals, then

the lines are perpendicular.

 If two nonvertical lines in the same plane are perpendicular, then their slopes are

negative reciprocals of each other.

 What is the negative reciprocal of 6? _________

Example: Determine whether any lines are  or :

 means parallel and

 means perpendicular

Line a: y = 5x – 3

Line b: x + 5y = 2

Line c: -10y – 2x = 0

Step 1: Calculate slopes:

Step 2: Compare slopes (same slopes  ; negative reciprocals  )

Conclusion:

Example: Write an equation of the line that passes through (4, -5) and is perpendicular to

the line y = 2x + 3.

Step 1: Determine the slope of the perpendicular line

Slope of original line: __________

Slope of perpendicular line: ____________

Step 2: Write the equation using point (4, -5) and the slope of the perpendicular line.

You try: Write an equation of the line in standard form through the given point…

…that is parallel to the given line.

y = -2x + 1; (-1, 2)

-3x + y = 7; (4, -2)

…that is is perpendicular to the given line.

y = -(1/2)x + 1; (0, -3)

5x + y = 1; (10, -1)

Standard Form Page 2