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Characteristics of Parallel LinesParallel lines: Are lines that do not intersectHave different y-intercepts

- Click on the picture below to see a video on how to write a parallel line to another lineusing point-slope form

04/2014L. Hojnowski 20144Parallel Lines- JMAP VideoTry Again04/2014L. Hojnowski 201449Try AgainQuiz Question #2Quiz Question #1Quiz Question #4Quiz Question #3Quiz Question #5Quiz Question #6Quiz Question #7Be careful of your signs when you are solving.

Parallel lines have the same slope. Parallel Lines- Example 104/2014L. Hojnowski 20146Example 1: Write an equation in slope-intercept form for the line that passes through (-2, 2) and is parallel to y = 4x 2. **Use the point-slope formula**

The equation is in slope-intercept form, m = 43) y 2 = 4 (x + 2) y y1 = m (x x1) y 2 = 4x + 8y 2 = 4 (x - - 2) +2 +2

y 2 = 4 (x + 2) 4) y = 4x + 10 STEPS:Rewrite the given equation into slope-intercept from (y = mx + b), if necessary, and identify the slope (m)Plug in the given point and the parallel slope (found in step 1) in the point-slope formula (y y1 = m (x x1)Distribute and simplify (if necessary)Solve for y

Try Again04/2014L. Hojnowski 201441Try AgainQuiz Question #2Quiz Question #1Quiz Question #4Quiz Question #3Quiz Question #5Quiz Question #6The slope in the equation is the reciprocal of the slope given in the problem. Perpendicular slopes are the negative reciprocals.Parallel Lines- Example 304/2014L. Hojnowski 20148Example 3: Write an equation in slope-intercept form for the line that passes through (-1, 6) and is parallel to 3x + y = 12. **Use the point-slope formula**

The equation is NOT in slope-intercept form, m = ? 3) y 6 = -3 (x -1) **In order to identify the slope, solve for y! y 6 = -3 (x + 1) 3x + y = 12 y 6 = -3x - 3-3x -3xy = -3x +12

m = -3 4) y 6 = -3x - 3 +6 +62) y y1 = m (x x1) y = -3x +3 y 6 = -3 (x -1)

Example of a given point and a lineTry Again04/2014L. Hojnowski 201442Try AgainQuiz Question #2Quiz Question #1Quiz Question #4Quiz Question #3Quiz Question #5Quiz Question #6The slope in the equation is the negative of the slope given in the problem. Perpendicular slopes are the negative reciprocals.

Also, be careful of your signs when multiplying.Perpendicular Lines- Example 104/2014L. Hojnowski 201411Example 1: Write an equation in slope-intercept form for the line that passes through (4, 2) and is perpendicular to y = (1/2)x + 1. **Use the point-slope formula**

The equation is in slope-intercept form, m = (1/2)3) y 2 = -2 (x - 4) Perpendicular slope: -2 y 2 = -2x + 82) y y1 = m (x x1) + 2 + 2 y 2 = -2 (x - 4) 4) y= -2x + 10 STEPS:Rewrite the given equation into slope-intercept from (y = mx + b), if necessary, and identify the slope (m)Plug in the given point and the perpendicular slope (negative reciprocal) in the point-slope formula (y y1 = m (x x1)Distribute and simplify (if necessary)Solve for yQuiz Question # 76. Determine whether 3x + 5y = 10 and 5x 3y= -6 are parallel, perpendicular, or neither.

a. neither b. parallel c. perpendicular04/2014L. Hojnowski 201447Perpendicular Lines- StepsGiven a point and an equation04/2014L. Hojnowski 201410Steps to writing a perpendicular l lineSTEPS:Rewrite the given equation into slope-intercept from (y = mx + b), if necessary, and identify the slope (m)Plug in the given point and the perpendicular slope (negative reciprocal) in the point-slope formula (y y1 = m (x x1)Distribute and simplify (if necessary)Solve for y

Characteristics of Perpendicular Lines04/2014L. Hojnowski 20149Perpendicular Lines: Are lines that intersect at right anglesHave negative reciprocal slopes-Example: m = 2 m = -1/2

- Click on the picture below to see a video to review how to write a perpendicular line to another line using slope-intercept form (you can use point-slope formula just like parallel lines)Perpendicular Lines- JMAP VideoPerpendicular Lines- Example 204/2014L. Hojnowski 201412Example 2: Write an equation in slope-intercept form for the line that passes through (-5, -1) and is perpendicular to y = (5/2)x - 3. **Use the point-slope formula**

The equation is in slope-intercept form, m = (5/2)3) y + 1= (-2/5) (x + 5)Perpendicular slope: (-2/5) y + 1= (-2/5)x - 2y y1 = m (x x1) - 1 - 1y -1 = (-2/5) (x - - 5) 4) y= (-2/5)x - 3 STEPS:Rewrite the given equation into slope-intercept from (y = mx + b), if necessary, and identify the slope (m)Plug in the given point and the perpendicular slope (negative reciprocal) in the point-slope formula (y y1 = m (x x1)Distribute and simplify (if necessary)Solve for yParallel Lines- Example 204/2014L. Hojnowski 20147Example 2: Write an equation in slope-intercept form for the line that passes through (6, 4) and is parallel to y = (1/3)x + 1. **Use the point-slope formula**

The equation is in slope-intercept form, m = 1/33) y 4 = (1/3) (x - 6) y y1 = m (x x1) y 4 = (1/3)x - 2y 4 = (1/3) (x - 6) +4 +4

4) y = (1/3)x + 2 STEPS:Rewrite the given equation into slope-intercept from (y = mx + b), if necessary, and identify the slope (m)Plug in the given point and the parallel slope (found in step 1) in the point-slope formula (y y1 = m (x x1)Distribute and simplify (if necessary)Solve for y

Parallel Lines- StepsGiven a point and an equation04/2014L. Hojnowski 20145Steps to writing a parallel lineSTEPS:Rewrite the given equation into slope-intercept from (y = mx + b), if necessary, and identify the slope (m)Plug in the given point and the parallel slope (found in step 1) in the point-slope formula (y y1 = m (x x1)Distribute and simplify (if necessary)Solve for y

ReferencesMcGraw-Hill Companies. (2014). Glencoe Algebra 1 Common Core Edition. New York: McGraw Hill.Seminars.usb.ac.ir. (2011). Hitting the objectives, Retrieved on September 14th, 2012, fromhttp://www.teambuildinggames.org/role-of-the-team-building-facilitator.Smiley Face, Retrieved on September 14th, 2012, from http://ed101.bu.edu/StudentDoc/current/ED101fa10/rajensen/images/happy-face1.png. Wee, E. (2011). Try again, Retrieved on September 15th, 2012, from http://radionjournals.blogspot.com/2011/04/try-again-part-3-caring-for-children.html.

04/2014L. Hojnowski 201451Reference from the dictionary Example 3: Write an equation in slope-intercept form for the line that passes through (-4, 6) and is perpendicular to 2x + 3y = 12. **Use the point-slope formula**

1) The equation is NOT in slope-intercept form, m = ?**In order to identify the slope, solve for y!2x + 3y = 12 2) y y1 = m (x x1) 3) y 6 = (3/2)(x + 4) -2x -2x y 6 = (3/2)(x -4) y 6 = (3/2)x + 63y = -2x + 12+ 6 + 6 3y = (-2/3)x + 4 4) y = (3/2)x + 12m = -2/3Perpendicular slope: (3/2)

Perpendicular Lines- Example 304/2014L. Hojnowski 201413Given a Point and a LineQuiz Question # 5 04/2014L. Hojnowski 2014385. Write an equation in slope-intercept form for the line that passes through (-8, 0) and is perpendicular to y = (-1/2)x - 4

a. y = (-1/2)x - 4b. y = 2x + 16c. y = -2x - 16 d. y = (1/2)x + 4

Determine whether parallel, perpendicular, or neither- Steps04/2014L. Hojnowski 201414STEPS:Rewrite both equation into slope-intercept form (y = mx + b) and identify each slopeCompare the slopes to see if they are the same, negative reciprocal, or neitherExample of Parallel Lines- Same SlopeExample of Perpendicular l Lines- Negative Reciprocal SlopeExample of Neither Parallel or Perpendicular LinesDetermine whether parallel, perpendicular, or neither- Example 104/2014L. Hojnowski 201415Example1: Determine whether the graphs of the pair of equations are parallel, perpendicular, or neither. 3x + 5y = 105x 3y = -6STEPS:Rewrite both equation into slope-intercept form (y = mx + b) and identify each slopeCompare the slopes to see if they are the same, negative reciprocal, or neither5x 3y = -6-5x -5x-3y = -5x - 6 -3 -3y = (-5/-3)x + 2m = (5/3)

3x + 5y = 10-3x -3x5y = -3x + 10 5 5y = (-3/5)x + 2m = (-3/5)

PERPENDICULAR- they have negative reciprocal slopesDetermine whether parallel, perpendicular, or neither- Example 204/2014L. Hojnowski 201416Example 2: Determine whether the graphs of the pair of equations are parallel, perpendicular, or neither. 2x - 8y = -24 x 4y = 4STEPS:Rewrite both equation into slope-intercept form (y = mx + b) and identify each slopeCompare the slopes to see if they are the same, negative reciprocal, or neitherPARALLEL- they have the same slopex 4y = 4 -x -x-4y = -x + 4 -4 -4y = (-1/-4)x - 1m = (1/4)

2x - 8y = -24 -2x -2x-8y = -2x - 24 -8 -8y = (-2/-8)x + 3m = (1/4)

Determine whether parallel, perpendicular, or neither- Example 304/2014L. Hojnowski 201417Example 3: Determine whether the graphs of the pair of equations are parallel, perpendicular, or neither. -3x + 4y = 8 -4x + 3y = -6NEITHER- they arent the same slopeand are not negative reciprocals

They are reciprocals but not negative reciprocals-4x + 3y = -6 +4x +4x3y = 4x - 6 3 3y = (4/3)x - 2m = (4/3)

-3x + 4y = 8 +3x +3x4y = 3x + 8 4 4y = (3/4)x + 2m = (3/4)

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