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 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. –T–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

You try it!! 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... REMEMBER Change the sign And Flip it over.

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

Examples

Name the slope of each line, then Give the PARALLEL slope and the PERPENDICULAR slope. Equation m // m m y = 3x + 5 7x + y = 4 y = 2 x = -4

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

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. Example 5 5. Write an equation that is PARALLEL to the given line passing through the given point. New // Equation

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 Parallel Lines Have SAME Slope (m) But… DIFFERENT Y-int. (b) Example 6

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

8. y = 3x – 2; (6, -1) 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. Perpendicular Lines Have OPPOSITE Slope (m) AND…. DIFFERENT Y-int. (b)

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) Example 9

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) No y-int, but “x”-int. Example 10