Parallel Lines •. Non-vertical lines are. parallel if and only if they

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Presentation transcript:

Parallel Lines •. Non-vertical lines are. parallel if and only if they Parallel Lines • Non-vertical lines are parallel if and only if they have the same slope.

Parallel Lines • All vertical lines are parallel.

Perpendicular Lines •. Diagonal (oblique) lines Perpendicular Lines • Diagonal (oblique) lines are  if and only if their slopes are opposite reciprocals. • For example, slopes of ¾ and -4/3 would make  lines.

Perpendicular Lines •. Another way to say this is Perpendicular Lines • Another way to say this is that the product of the slopes is -1. • For example, ¾  -4/3 = -1, so the lines are .

Perpendicular Lines

Perpendicular Lines •. Any vertical line and any. horizontal line are Perpendicular Lines • Any vertical line and any horizontal line are perpendicular.

Are these lines parallel, perpendicular, or neither. y = 6x – 2 Are these lines parallel, perpendicular, or neither? y = 6x – 2 y + 4 = 1/6(x – 3)

Are these lines parallel, perpendicular, or neither. y = 6x – 2. m = 6 Are these lines parallel, perpendicular, or neither? y = 6x – 2 m = 6 y + 4 = 1/6(x – 3) m = 1/6 Neither

Are these lines parallel, perpendicular, or neither. y – 2 = ½(x + 1) Are these lines parallel, perpendicular, or neither? y – 2 = ½(x + 1) y = ½x + 5

Are these lines parallel, perpendicular, or neither. y – 2 = ½(x + 1) Are these lines parallel, perpendicular, or neither? y – 2 = ½(x + 1) m = ½ y = ½x + 5 m = ½ Parallel

Write the equation of a line through the point (5,-6) that is perpendicular to the line y = 4x – 9

Write the equation of a line through the point (5,-6) that is perpendicular to the line y = 4x – 9 Slope of this line = 4 Slope of  line = -¼

Write the equation of a line through the point (5,-6) that is perpendicular to the line y = 4x – 9 y + 6 = -¼(x – 5)

Write the equation of a line through the point (-2,3) that is parallel to the line x = 4

Write the equation of a line through the point (-2,3) that is parallel to the line x = 4 This is a vertical line The answer is x = -2 .

REMEMBER … •. Parallel … same slope •. Perpendicular … opposite REMEMBER … • Parallel … same slope • Perpendicular … opposite reciprocals

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