Sec 3 7 Slopes of Parallel Perpendicular Lines

  • Slides: 15
Download presentation
Sec. 3 -7 Slopes of Parallel & Perpendicular Lines Objectives: 1) To relate slope

Sec. 3 -7 Slopes of Parallel & Perpendicular Lines Objectives: 1) To relate slope and // lines. 2) To relate slope & lines

Rules for m of // and Lines n Slopes of // lines are the

Rules for m of // and Lines n Slopes of // lines are the same. – // lines have equal slopes. n Slopes of lines are flipped and reversed. – Opposite reciprocals – Example: If one line has a slope of ½, then the line to it has a slope of -2/1.

If the lines are perpendicular then: m 1 m 2 = -1 So if

If the lines are perpendicular then: m 1 m 2 = -1 So if the slope of the first line is 3/8, then the slope of the second is ____ Just flip the first slope and change its sign

On the corner of your notes write down whether each of the next few

On the corner of your notes write down whether each of the next few pairs of lines are parallel, perpendicular, or neither.

1. slope of line r = slope of line s = These lines are

1. slope of line r = slope of line s = These lines are parallel.

2. slope of line t = slope of line u = These lines are

2. slope of line t = slope of line u = These lines are does m m = -1 ? perpendicular. 1 2

3. slope of line t = slope of line u = These lines are

3. slope of line t = slope of line u = These lines are parallel.

4. slope of line t = slope of line u = NEITHER!! Slopes aretonot

4. slope of line t = slope of line u = NEITHER!! Slopes aretonot Do the two slopes multiply makeor-1? congruent opposite reciprocals of each other.

5. slope of line t = slope of line u = 7 Perpendicular. 7.

5. slope of line t = slope of line u = 7 Perpendicular. 7. = -1

Example 1: n Are the following lines parallel? – 4 y – 12 x

Example 1: n Are the following lines parallel? – 4 y – 12 x = 20 – y = 3 x – 1 n Put them both in y-intercept form y = mx + b n See if their slopes are the same, if so then they are //. y = -3 x + 1 -4 y – 12 x = 20 -4 y = 12 x + 20 y =-3 x + 5 Slopes are equal, so the lines are //.

Example 2: n Line r contains points P(0, 3) & Q(-2, 5). Line t

Example 2: n Line r contains points P(0, 3) & Q(-2, 5). Line t contains points R(0, -7) & S(3, -10). Are they //, , or neither? x 1 y 1 x 2 y 2 (0, 3) and (-2, 5) m = (y 2 – y 1)/(x 2 – x 1) = (5 – 3)/(-2 – 0) = 2/-2 = -1 x 1 y 2 -7) (0, x 2 and (3, -10) m = (y 2 – y 1)/(x 2 – x 1) = (-10 – (-7))/(3 - 0) = -3/3 = -1 Slopes are equal so the lines are //

Example 3: n Write an equation in point – slope form for the line

Example 3: n Write an equation in point – slope form for the line parallel to 6 x – 3 y = 9 that contains point (-5, -8). – Step 1: Find the slope of the given line. 6 x – 3 y = 9 -3 y = -6 x + 9 y – y 1 = m(x – x 1) y = 2 x - 3 Plug 2 in for m in the formula & plug in the point. x 1 y 1 (-5, -8) y – (-8) = 2(x – (-5)) y + 8 = 2 x + 10 y = 2 x + 2

Example 4: an equation for the line to 3 x + y = -5

Example 4: an equation for the line to 3 x + y = -5 that contains the point (-3, 7). n Write Step 1: Find slope of given line then flip and reverse it. Step 2: Plug in your m and the point. x 1 y 1 (-3, 7) 3 x + y = -5 y – y 1 = m(x – x 1) y = -3 x – 5 y – 7 = 1/3(x – (-3)) m = -3 y – 7 = (1/3)x + 1 m = 1/3 y = (1/3)x + 8

Use what you learned! n Are the following lines //, , or neither? y

Use what you learned! n Are the following lines //, , or neither? y = 1/2 x + 3 n y = 2 x + 4 n n Neither n Are the following lines //, , or neither? 8 y = -2 x – 5 n y – 4 x = 7 n y = (-1/4)x – (5/8) n y = 4 x + 7 n n

PARALLEL AND PERPENDICULAR LINES Slopes Parallel Lines ThePARALLEL AND PERPENDICULAR LINES Slopes Parallel Lines The
Slopesofof Paralleland and Perpendicular Slopes Lines Perpendicular LinesSlopesofof Paralleland and Perpendicular Slopes Lines Perpendicular Lines
Slopesofof Paralleland and Perpendicular Slopes Lines Perpendicular LinesSlopesofof Paralleland and Perpendicular Slopes Lines Perpendicular Lines
Parallel Perpendicular Lines Parallel and Perpendicular Lines TheParallel Perpendicular Lines Parallel and Perpendicular Lines The
Parallel and Perpendicular Lines Parallel and Perpendicular LinesParallel and Perpendicular Lines Parallel and Perpendicular Lines
Parallel and Perpendicular Lines Parallel Lines Two linesParallel and Perpendicular Lines Parallel Lines Two lines
Parallel and Perpendicular Assignment Parallel Lines Parallel linesParallel and Perpendicular Assignment Parallel Lines Parallel lines
Parallel and Perpendicular Lines Parallel Line Perpendicular lineParallel and Perpendicular Lines Parallel Line Perpendicular line
Parallel Perpendicular Lines Slope of Parallel Lines TwoParallel Perpendicular Lines Slope of Parallel Lines Two
Parallel and Perpendicular Lines Slope of Parallel LinesParallel and Perpendicular Lines Slope of Parallel Lines
Parallel and Perpendicular Lines Objectives Define parallel linesParallel and Perpendicular Lines Objectives Define parallel lines
Parallel Perpendicular Lines Parallel and Lines Transversals ReviewParallel Perpendicular Lines Parallel and Lines Transversals Review
Parallel and Perpendicular Lines Parallel Lines l AllParallel and Perpendicular Lines Parallel Lines l All
Parallel and Perpendicular Lines Parallel Lines Two nonverticalParallel and Perpendicular Lines Parallel Lines Two nonvertical