Parallel & Perpendicular Lines

Real World Application How do you get the ball in the hole?

Lesson Objectives 1) Identify lines that are parallel and perpendicular. 2) Find parallel and perpendicular slopes of linear equations. 3) Write linear equations of lines that are parallel and perpendicular using a point, y-intercept and horizontal and vertical lines.

Review Opposite Operation – 3x = 9 + 3 + 3 + 3 Don’t add 3 to both sides.

Review Opposite Operation – 3x = 9 – 3 – 3 – 3 Divide by – 3 on both sides.

Parallel Lines ( ) - 2 different lines that have the same slope. Definition Parallel Lines ( ) - 2 different lines that have the same slope. same slope slope = 3 slope (m) = 3 slope = – 4 slope (m) = – 4

1) Are these lines Parallel? Example 1) Are these lines Parallel? -1 -3 -2 -4 -5 1 2 3 4 5 – 2 – 1 = 2 -2 -2 +2 +2 – 2 – 1 = -2 -2 2 +2 +2 Yes

Example 2) Write an equation in slope-intercept form of a line parallel to y = – x + 6 with a y-intercept of – 4. parallel y = – x + 6 – 4 y = – x + 6 1 –1 Same Slope y = mx + b m b y = – 1 x + b y = – 1x – 4

Whiteboard Practice 3) Write an equation in slope-intercept form of a line parallel to y = –2x + 1 with a y-intercept of – 6. parallel y = –2x + 1 – 6 y = – 2x + 1 – 2 Same Slope y = mx + b m b y = – 2 x + b y = – 2x – 6

Whiteboard Practice 4) Write an equation in slope-intercept form of a line parallel to y = –3x – 7 with a y-intercept of 8. parallel y = –3x – 7 8 y = – 3x – 7 – 3 Same Slope y = mx + b m b y = – 3 x + b y = – 3x + 8

Real World Application Knowing the how the ball will come off the wall (perpendicular angle) will help you sink the ball.

Real World Application Knowing the how the ball will come off the wall (perpendicular angle) will help you sink the ball.

Real World Application Knowing the how the ball will come off the wall (perpendicular angle) will help you sink the ball.

Definition/Example Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m Opposite Opposite 5) slope (m) = 3 3 Reciprocal Reciprocal slope = – 3 – 3 1 1

Definition/Example Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m Opposite 5) slope (m) = 3 Reciprocal slope = – 3 1 1 – 3

Whiteboard Practice 6) Line b has a slope (m) = – 2 – 2 What is the perpendicular slope of line b? slope = – 2 + 2 Opposite Opposite Reciprocal Reciprocal 1 1 Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

Whiteboard Practice 6) Line b has a slope (m) = – 2 What is the perpendicular slope of line b? slope = – 2 1 Opposite Reciprocal 1 + 2 Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

Example 7) Line f has a slope (m) = – 7 – 7 What is the perpendicular slope of line f ? slope = – 7 + 7 Opposite Opposite Reciprocal Reciprocal 1 1 Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

Example 7) Line f has a slope (m) = – 7 What is the perpendicular slope of line f ? slope = – 7 1 Opposite Reciprocal 1 + 7 Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

Example 8) Line k has a slope (m) = - 5 2 - 5 2 8) Line k has a slope (m) = What is the perpendicular slope of line k ? 5 slope = - Opposite Opposite 2 Reciprocal Reciprocal Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

Example 8) Line k has a slope (m) = – 5 2 8) Line k has a slope (m) = What is the perpendicular slope of line k ? 2 slope = Opposite 5 Reciprocal Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

Example 3 2 3 2 9) Line p has a slope of and line r has a slope of Are the two lines parallel, perpendicular or neither? – 2 3 – 2 3 3 3 2 Same Slope? No slope = 2 Perpendicular Slope? – 2 Yes slope = 3 3 3 – 2 Opposite Opposite = Reciprocal Reciprocal 2 2 3

Whiteboard Practice 10) Line j has a slope (m) = 7 3 7 3 10) Line j has a slope (m) = What is the perpendicular slope of line j ? 7 – slope = Opposite Opposite 3 Reciprocal Reciprocal Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

Whiteboard Practice 10) Line j has a slope (m) = 7 3 10) Line j has a slope (m) = What is the perpendicular slope of line j ? 3 – slope = Opposite 7 Reciprocal Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

Whiteboard Practice 1 6 1 6 11) Line t has a slope of and line p has a slope of Are the two lines parallel, perpendicular or neither? – 1 6 – 1 6 1 6 1 Same Slope? No slope = 6 Perpendicular Slope? – 1 No slope = 6 1 1 – 6 Opposite Opposite = Reciprocal Reciprocal 6 6 1

Whiteboard Practice 12) Line w has a slope (m) = – 5 – 5 What is the perpendicular slope of line w ? slope = – 5 + 5 Opposite Opposite Reciprocal Reciprocal 1 1 Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

Example 12) Line w has a slope (m) = – 5 What is the perpendicular slope of line w ? slope = – 5 1 Opposite Reciprocal 1 + 5 Perpendicular Lines ( ) - one line has a slope of m and the other line has a slope of – 1 m

13) Are these lines Perpendicular? Whiteboard Practice 13) Are these lines Perpendicular? Yes -1 -3 -2 -4 -5 1 2 3 4 5 3 3 2 +2 +2 = 2 +3 +3 – 2 – 3 2 = -2 -2 3 +3 +3

Example 14) Write an equation in slope-intercept form of a line that has a y-intercept of – 5 & that is perpendicular to the line y = – 3x + 4. – 5 perpendicular y = – 3x + 4 – 3 y = mx + b slope (m) = – 3 – 3 m b + 3 slope = – 3 1 1 Opposite Opposite Reciprocal Reciprocal

Example 14) Write an equation in slope-intercept form of a line that has a y-intercept of – 5 & that is perpendicular to the line y = – 3x + 4. – 5 y = mx + b slope (m) = – 3 m b 1 + 3 1 slope = – 3 1 + 3 1 3 y = x + – 5 b

Example 14) Write an equation in slope-intercept form of a line that has a y-intercept of – 5 & that is perpendicular to the line y = – 3x + 4. y = mx + b slope (m) = – 3 m b 1 slope = – 3 1 + 3 1 3 y = x – 5

Whiteboard Practice 15) Write an equation in slope-intercept form of a line that has a y-intercept of 3 & that is perpendicular to the line y = – 7x – 2. 3 perpendicular y = – 7x – 2 – 7 y = mx + b slope (m) = – 7 – 7 m b + 7 slope = – 7 1 1 Opposite Opposite Reciprocal Reciprocal

Whiteboard Practice 15) Write an equation in slope-intercept form of a line that has a y-intercept of 3 & that is perpendicular to the line y = – 7x – 2. 3 y = mx + b slope (m) = – 7 m b 1 1 + 7 slope = – 7 1 + 7 1 7 y = x + 3 b

Whiteboard Practice 15) Write an equation in slope-intercept form of a line that has a y-intercept of 3 & that is perpendicular to the line y = – 7x – 2. y = mx + b slope (m) = – 7 m b 1 slope = – 7 1 + 7 1 7 y = x + 3

Example 16) Write an equation in slope-intercept form of a line that passes through the point (4,– 9) & that is perpendicular to the line y = 2x + 3. 4 – 9 perpendicular y = 2x + 3 2 y = mx + b slope (m) = 2 2 m b – – 2 slope = 2 1 1 Opposite Opposite Reciprocal Reciprocal

Example 16) Write an equation in slope-intercept form of a line that passes through the point (4,– 9) & that is perpendicular to the line y = 2x + 3. 4 – 9 y = mx + b slope (m) = 2 m b – 1 – 2 1 slope = 2 1 – 2 1 2 – y = x + b

Example 16) Write an equation in slope-intercept form of a line that passes through the point (4,– 9) & that is perpendicular to the line y = 2x + 3. 4 – 9 y = mx + b 1 2 m b – y = x + – 7 b – 9 = – 2 + b + 2 + 2 + 2 1 2 – – 9 = (4) + b – 7 – 7 = b

Example 16) Write an equation in slope-intercept form of a line that passes through the point (4,– 9) & that is perpendicular to the line y = 2x + 3. y = mx + b 1 2 m b – y = x – 7 – 9 = – 2 + b + 2 + 2 1 2 – – 9 = (4) + b – 7 – 7 = b

Whiteboard Practice y = mx + b slope (m) = – 1 – 1 m b slope = – 1 – 1 17) Write an equation in slope-intercept form of a line that passes through the point (1,– 3) & that is parallel to the line y = – x + . 1 – 3 parallel 1 6 1 6 y = – x + 1 –1 y = mx + b slope (m) = – 1 – 1 m b slope = – 1 – 1 Same slope 1 y = – x + b

Whiteboard Practice y = mx + b m b y = – x + – 2 b – 3 = – 1 + b – 3 = 17) Write an equation in slope-intercept form of a line that passes through the point (1,– 3) & that is parallel to the line y = – x + . 1 – 3 1 6 1 y = mx + b m b y = – x + – 2 b – 3 = – 1 + b – 3 = (1) + b – + 1 + 1 + 1 – 2 – 2 = b

Whiteboard Practice y = mx + b m b y = – x – 2 – 3 = – 1 + b – 3 = (1) 17) Write an equation in slope-intercept form of a line that passes through the point (1,– 3) & that is parallel to the line y = – x + . 1 6 1 y = mx + b m b y = – x – 2 – 3 = – 1 + b – 3 = (1) + b – + 1 + 1 – 2 = b

Example y = mx + b m b slope (m) = slope = 1 4 1 Same slope 4 y = x + 18) Write an equation in slope-intercept form of a line that passes through the point (3,8) & that is parallel to the line y = x – 3. 3 8 parallel 1 4 1 4 y = x – 3 y = mx + b m b 1 4 1 4 slope (m) = slope = 1 4 1 Same slope 4 1 4 y = x + b

Example y = mx + b m b y = x + – 4 b 8 = 12 + b – 12 – 12 – 12 8 = (3) 18) Write an equation in slope-intercept form of a line that passes through the point (3,8) & that is parallel to the line y = x – 3. 3 8 1 4 y = mx + b m b 1 4 y = x + – 4 b 8 = 12 + b – 12 – 12 – 12 1 4 8 = (3) + b – 4 – 4 = b

Example y = mx + b m b y = x – 4 8 = 12 + b – 12 – 12 8 = (3) + b – 4 18) Write an equation in slope-intercept form of a line that passes through the point (3,8) & that is parallel to the line y = x – 3. 1 4 y = mx + b m b 1 4 y = x – 4 8 = 12 + b – 12 – 12 1 4 8 = (3) + b – 4 – 4 = b

Whiteboard Practice y = mx + b m b slope (m) = – – 3 slope = 3 7 7 19) Write an equation in slope-intercept form of a line that passes through the point (6,– 5) & that is perpendicular to the line y = x – 2. 6 – 5 perpendicular 3 7 3 7 y = x – 2 y = mx + b m b Opposite Opposite 3 7 3 7 slope (m) = Reciprocal Reciprocal – – 3 slope = 3 7 7

Whiteboard Practice y = mx + b m b slope (m) = – 7 – 3 7 slope = 3 7 19) Write an equation in slope-intercept form of a line that passes through the point (6,– 5) & that is perpendicular to the line y = x – 2. 6 – 5 perpendicular 3 7 y = mx + b m b Opposite – 3 7 slope (m) = Reciprocal – 7 – 3 7 slope = 3 7 – 3 7 3 – y = x + b

Whiteboard Practice y = mx + b m b y = x + 9 b – 5 = – 14 + b + 14 19) Write an equation in slope-intercept form of a line that passes through the point (6,– 5) & that is perpendicular to the line y = x – 2. 6 – 5 3 7 y = mx + b m b – 7 3 y = x + 9 b – 5 = – 14 + b + 14 + 14 + 14 – 7 3 9 9 = b – 5 = (6) + b

Whiteboard Practice y = mx + b m b y = x + 9 – 5 = – 14 + b + 14 + 14 19) Write an equation in slope-intercept form of a line that passes through the point (6,– 5) & that is perpendicular to the line y = x – 2. 3 7 y = mx + b m b – 7 3 y = x + 9 – 5 = – 14 + b + 14 + 14 – 7 3 9 9 = b – 5 = (6) + b

Example y = mx + b slope (m) = 3 3 m b slope = 3 3 Same slope 1 y = 3 20) Write an equation in slope-intercept form of a line that passes through the point (2,7) & that is parallel to the line y = 3x + 4. 2 7 parallel y = 3x + 4 3 y = mx + b slope (m) = 3 3 m b slope = 3 3 Same slope 1 y = 3 x + b

Example y = mx + b m b y = 3x + 1 b 7 = 6 + b 7 = (2) + b 3 – 6 – 6 20) Write an equation in slope-intercept form of a line that passes through the point (2,7) & that is parallel to the line y = 3x + 4. 2 7 y = mx + b m b y = 3x + 1 b 7 = 6 + b 7 = (2) + b 3 – 6 – 6 – 6 1 1 = b

Example y = mx + b m b y = 3x + 1 7 = 6 + b 7 = (2) + b 3 – 6 – 6 1 = 20) Write an equation in slope-intercept form of a line that passes through the point (2,7) & that is parallel to the line y = 3x + 4. y = mx + b m b y = 3x + 1 7 = 6 + b 7 = (2) + b 3 – 6 – 6 1 = b

Whiteboard Practice 21) Write an equation in slope-intercept form of a line that passes through the point (10,– 4) & that is perpendicular to the line y = – 5x + 7. 10 – 4 perpendicular y = – 5x + 7 – 5 y = mx + b slope (m) = – 5 – 5 m b 5 slope = – 5 1 1 Opposite Opposite Reciprocal Reciprocal

Whiteboard Practice 21) Write an equation in slope-intercept form of a line that passes through the point (10,– 4) & that is perpendicular to the line y = – 5x + 7. 10 – 4 y = mx + b slope (m) = – 5 m b - 1 1 5 slope = 5 1 5 1 5 y = x + b

Whiteboard Practice 21) Write an equation in slope-intercept form of a line that passes through the point (10,– 4) & that is perpendicular to the line y = – 5x + 7. 10 – 4 y = mx + b 1 5 m b y = x + – 6 b – 4 = 2 + b – 2 – 2 – 2 1 5 – 4 = (10) + b – 6 – 6 = b

Whiteboard Practice 21) Write an equation in slope-intercept form of a line that passes through the point (10,– 4) & that is perpendicular to the line y = – 5x + 7. y = mx + b 1 5 m b y = x – 6 – 4 = 2 + b – 2 – 2 1 5 – 4 = (10) + b – 6 – 6 = b

Whiteboard Practice y = mx + b m b slope (m) = slope = – 1 3 – 1 22) Write an equation in slope-intercept form of a line that passes through the point (– 4,2) & that is parallel to the line y = x – . – 4 2 parallel – 1 3 – 1 3 7 8 7 8 y = x – y = mx + b m b – 1 3 – 1 3 slope (m) = slope = – 1 3 – 1 Same slope 3 1 3 – y = x + b

Whiteboard Practice y = mx + b m b 2 = + b y = x + b 2 = (–4) + b = b 22) Write an equation in slope-intercept form of a line that passes through the point (– 4,2) & that is parallel to the line y = x – . – 4 2 – 1 3 7 8 y = mx + b m b 4 3 2 = + b – 1 3 2 3 y = x + b 6 3 4 3 – 4 3 – 4 3 – – 1 3 2 = (–4) + b 2 3 2 3 = b

Whiteboard Practice y = mx + b m b 2 = + b y = x + 2 = (–4) + b = b 22) Write an equation in slope-intercept form of a line that passes through the point (– 4,2) & that is parallel to the line y = x – . – 1 3 7 8 y = mx + b m b 4 3 2 = + b – 1 3 2 3 y = x + 6 3 4 3 – 4 3 – – 1 3 2 = (–4) + b 2 3 2 3 = b

Example y = mx + b m b slope (m) = 2 slope = – 2 3 3 23) Write an equation in slope-intercept form of a line that passes through the point (3,4) & that is perpendicular to the line y = x – . 3 4 perpendicular – 2 3 – 2 3 4 5 4 5 y = x – y = mx + b m b Opposite Opposite – 2 3 – 2 3 slope (m) = Reciprocal Reciprocal 2 slope = – 2 3 3

Example y = mx + b m b slope (m) = 3 2 3 slope = – 2 3 2 y = x + b 23) Write an equation in slope-intercept form of a line that passes through the point (3,4) & that is perpendicular to the line y = x – . 3 4 perpendicular – 2 3 4 5 y = mx + b m b Opposite – 2 3 slope (m) = Reciprocal 3 2 3 slope = – 2 3 2 3 2 y = x + b

Example y = mx + b m b 4 = + b y = x + b 4 = (3) + b = b 23) Write an equation in slope-intercept form of a line that passes through the point (3,4) & that is perpendicular to the line y = x – . 3 4 – 2 3 4 5 y = mx + b m b 9 2 4 = + b 3 2 1 2 – y = x + b 8 2 9 2 – 9 2 – 9 2 – 3 2 4 = (3) + b 1 2 – 1 2 – = b

Example y = mx + b m b 4 = + b y = x – 4 = (3) + b = b 23) Write an equation in slope-intercept form of a line that passes through the point (3,4) & that is perpendicular to the line y = x – . – 2 3 4 5 y = mx + b m b 9 2 4 = + b 3 2 1 2 y = x – 8 2 9 2 – 9 2 – 3 2 4 = (3) + b 1 2 – 1 2 - = b

Example 24) Write an equation in slope-intercept form of a line that has a y-intercept of – 3 & that is perpendicular to the line 3x + 2y = 10. – 3 y = mx + b 3x + 2y = 10 m 3x + 2y = 10 2y 10 – 3x – 3x – 3x 2y = – 3x + 10 2 2 2 2 2 3 2 – y = x + 5

Example 24) Write an equation in slope-intercept form of a line that has a y-intercept of – 3 & that is perpendicular to the line 3x + 2y = 10. – 3 perpendicular 3 2 – 3 2 – y = mx + b m b slope (m) = 3 2 – 3 slope = 2 Opposite Opposite Reciprocal Reciprocal

Example 24) Write an equation in slope-intercept form of a line that has a y-intercept of – 3 & that is perpendicular to the line 3x + 2y = 10. – 3 3 2 – y = mx + b m b slope (m) = 3 2 – 2 3 2 3 slope = 2 3 y = x + – 3 b

Example 24) Write an equation in slope-intercept form of a line that has a y-intercept of – 3 & that is perpendicular to the line 3x + 2y = 10. 3 2 – y = mx + b m b slope (m) = 3 2 – 2 3 slope = 2 3 y = x – 3

Whiteboard Practice 25) Write an equation in slope-intercept form of a line that has a y-intercept of 8 & that is perpendicular to the line – 8x + 2y = 12. 8 y = mx + b – 8x + 2y = 12 m – 8x + 2y = 12 2y 12 + 8x + 8x + 8x 2y = 8x + 12 2 2 2 2 2 y = 4 x + 6

Whiteboard Practice 25) Write an equation in slope-intercept form of a line that has a y-intercept of 8 & that is perpendicular to the line – 8x + 2y = 12. 8 perpendicular 4 1 4 y = mx + b m b slope (m) = 1 4 1 4 slope = – – 1 Opposite Opposite Reciprocal Reciprocal

Whiteboard Practice 25) Write an equation in slope-intercept form of a line that has a y-intercept of 8 & that is perpendicular to the line – 8x + 2y = 12. 8 4 1 y = mx + b m b slope (m) = 4 1 – 1 4 1 4 slope = – – 1 4 y = x + – 8 b

Whiteboard Practice 25) Write an equation in slope-intercept form of a line that has a y-intercept of 8 & that is perpendicular to the line – 8x + 2y = 12. 4 1 y = mx + b m b slope (m) = 4 1 – 1 4 slope = – 1 4 y = x + 8 –

Example 26) Write an equation in point-slope form for the line that contains the point (5,– 4) & that is perpendicular to the line – 18x + 3y = 15. 5 – 4 – 18x + 3y = 15 – 18x + 3y = 15 3y 15 + 18x + 18x + 18x 3y = 18x + 15 3 3 3 3 3 y = 6 x + 5

Example 26) Write an equation in point-slope form for the line that contains the point (5,– 4) & that is perpendicular to the line – 18x + 3y = 15. 5 – 4 perpendicular 6 1 6 slope (m) = 1 6 1 6 slope = – – 1 Opposite Opposite Reciprocal Reciprocal

Example 26) Write an equation in point-slope form for the line that contains the point (5,– 4) & that is perpendicular to the line – 18x + 3y = 15. 5 – 4 6 1 slope (m) = 6 1 – 1 6 1 6 slope = – – 1 6 – y – = – 4 y1 (x – ) x1 5

Example 26) Write an equation in point-slope form for the line that contains the point (5,– 4) & that is perpendicular to the line – 18x + 3y = 15. 6 1 slope (m) = 6 1 – 1 6 slope = – 1 6 – y + 4 = (x – 5)

Whiteboard Practice 27) Write an equation in point-slope form for the line that contains the point (– 2,6) & that is perpendicular to the line – 2 6 3 4 – 3 4 – y = x + 5 y = x + 5 3 4 – 3 4 – y = x + 5

Whiteboard Practice 27) Write an equation in point-slope form for the line that contains the point (– 2,6) & that is perpendicular to the line – 2 6 perpendicular 3 4 – 3 4 – slope (m) = 3 4 – 3 slope = 4 Opposite Opposite Reciprocal Reciprocal

Whiteboard Practice 27) Write an equation in point-slope form for the line that contains the point (– 2,6) & that is perpendicular to the line – 2 6 3 4 – slope (m) = 3 4 – 4 3 4 3 slope = 4 3 y – = y1 6 (x – ) – 2 x1

Whiteboard Practice 27) Write an equation in point-slope form for the line that contains the point (– 2,6) & that is perpendicular to the line 3 4 – slope (m) = 3 4 – 4 3 slope = 4 3 y – 6 = (x + 2)

Example 28) Write an equation in point-slope form for the line that contains the point (5,2) & that is perpendicular to the line 3y = 6. 5 2 3y = 6 3y = 6 3 3 3 y = 2

Example 28) y = 2 Special line ( ,2) – 3 ( ,2) 2 (x,y) y Rise Rise Run -1 -3 -2 -4 -5 1 2 3 4 5 ( ,2) – 3 (– 3,2) (2,2) ( ,2) 2 +5 +5 (x,y) y Rise Rise Run = = Run 5

Example 28) Write an equation in point-slope form for the line that contains the point (5,2) & that is perpendicular to the line 3y = 6. 5 2 1 slope (m) = 1 1 slope = – – 1

Example 28) Write an equation in point-slope form for the line that contains the point (5,2) & that is perpendicular to the line 3y = 6. 5 2 1 slope (m) = 1 – 1 slope = – u defined This line’s slope is

Review/Example 1 = You take the x value Special line (3, ) 2 (3, ) – 1 u defined = You take the x value Special line -1 -3 -2 -4 -5 1 2 3 4 5 (3, ) 2 (3,2) (3, ) – 1 (x,y) x (3,– 1) x = 3

Example 28) Write an equation in point-slope form for the line that contains the point (5,2) & that is perpendicular to the line 3y = 6. 5 2 Where are we going to get an x value on the line? x = x value 5

Example 28) Write an equation in point-slope form for the line that contains the point (5,2) & that is perpendicular to the line 3y = 6. Where are we going to get an x value on the line? x = 5

Whiteboard Practice 29) Graph the line that contains the point (– 3,4) & is perpendicular to the line – 3 4 2 3 2 3 -1 -3 -2 -4 -5 1 2 3 4 5 y = x + 2 y = x + 2. 2 3 2 3 slope (m) = 2 3 slope = – 2 – 3

Whiteboard Practice 29) Graph the line that contains the point (– 3,4) & is perpendicular to the line – 3 4 2 3 -1 -3 -2 -4 -5 1 2 3 4 5 y = x + 2. (– 3,4) 2 3 -3 slope (m) = +2 2 3 slope = – 3 3 Rise Rise Run – – = Run 2 2

Key Points & Don’t Forget When finding a perpendicular slope, don’t forget to do the opposite sign. (– 2 becomes positive)

The Assignment pg. 261-263 #’s 17-65 odd, 70-84 even

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