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Parallel and Perpendicular Lines

Parallel and Perpendicular Lines. Parallel Lines //. All parallel lines have the same slope. Parallel lines will NEVER have the same y-intercept. The slope of all vertical lines is undefined. (No Slope) The slope of all horizontal lines is zero. Perpendicular Lines.

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Parallel and Perpendicular Lines

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  1. Parallel and Perpendicular Lines

  2. Parallel Lines // • All parallel lines have the same slope. • Parallel lines will NEVER have the same y-intercept. • The slope of all vertical lines is undefined. (No Slope) • The slope of all horizontal lines is zero.

  3. Perpendicular Lines • Lines that form a 90° Angle. • Perpendicular Lines CAN have the same y-intercept IF that is where they cross. • Perpendicular Lines have slopes that are negative reciprocals. • This means to change the sign and flip the slope. Ex. If line “m” has a slope of 5, then it’s negative reciprocal is

  4. IF line “p” has a slope of -2, then a line to it has a slope of …… For line “n” the slope is the slope is... You try it!! REMEMBER Change the sign And Flip it over.

  5. Let’s compare Vertical and Horizontal Lines. • Vertical lines are ┴ to horizontal lines. AND • Horizontal lines are ┴ to vertical lines.

  6. Examples So..... The slope of line "v" is undefined. The slope is..... For line "d" if m=0 The slope is.....

  7. Name the slope of each line, thenGive the PARALLEL slope and thePERPENDICULAR slope.

  8. Why do we need to be able to identify the Parallel & Perpendicular Slopes? • So that we can write equations for new lines. • Either lines that are Parallel • OR lines that are Perpendicular

  9. Example 5 • HOW? • 1. Name the slope of the line you are given. • 2. List the new slope. • 3. Use the new slope and the point you are given in the slope-intercept formula to write a new equation. Like This... Write an equation that is PARALLEL to the given line passing through the given point. 5. New // Equation

  10. Example 6 Write an equation that is PARALLEL to the given line passing through the given point. 6. To get the Slope, solve For “y” • Find the PRGM key on your calculator. • Select program ASLOPE • Which option? • #2 because you have a point and a slope. • Enter NEW (parallel) slope • Enter X and Y from your ordered pair But… DIFFERENT Y-int. (b) Parallel Lines Have SAME Slope (m)

  11. Choose program ASLOPE Option #2 Name the slope Undefined – No number value – so….. Name the “x” coordinate in the ordered pair. 7. x = 5; (3, 4) But… DIFFERENT Y-int. (b) Parallel Lines Have SAME Slope (m) x = 3 No y-int, but different “x” Both are Undefined

  12. Choose program ASLOPE Option #2 Name the slope of this line but do not type it in. m = 3 What is perpendicular to 3? - 1/3 type this one in because you are looking for a perpendicular equation. Enter the X and Y from the ordered pair. Write an equation that is PERPENDICULAR to the given line passing through the given point. 8. y = 3x – 2; (6, -1) Perpendicular Lines Have OPPOSITE Slope (m) AND…. DIFFERENT Y-int. (b)

  13. Example 9 Write an equation that is PERPENDICULAR to the given line passing through the given point. 9. To get the Slope, solve For “y” • Find the PRGM key on your calculator. • Select program ASLOPE • Which option? • #2 because you have a point and a slope. • Enter NEW (perpendicular) slope • Enter X and Y from your ordered pair Perpendicular Lines Have OPPOSITE Slopes (m) AND…. DIFFERENT Y-int. (b)

  14. Example 10 10. y = 8; (-2, 8) • Choose program ASLOPE • Option #2 • Name the slope • ZERO – but don’t enter it yet. • What is perpendicular to ZERO? • Undefined – has no number value so… • Name the “x” coordinate in the ordered pair. Perpendicular Lines Have OPPOSITE Slopes (m) AND… DIFFERENT Y-int. (b) x = -2 No y-int, but “x”-int.

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