Algebra Monday December 6, 2010 EQ: How do we write equations in point-slope form?

Transcription

1 Algebra Monday December 6, 2010 EQ: How do we write equations in point-slope form? Homework Review: Complete Lesson 5-4 Extra Practice if you did not complete it in class today! AND pg. 310 #25-30; #

2 Homework Review: Complete Lesson 5-4 Extra Practice if you did not complete it in class today! AND pg. 310 #25-30; #

3 Homework Review: Complete Lesson 5-4 Extra Practice if you did not complete it in class today! AND pg. 310 #25-30; #

4 EQ: How do we write equations in point-slope form? What do these three terms have in common? Standard Slope - Intercept Point - Slope These are all forms of a linear equation! y - y 1 = m(x - x 1 ) what is y - that is the y in every linear equation what is y 1 - the y value from a given point what is m - is the slope what is x - that is the x in every linear equation what is x 1 - the x value from a given point What is the Point-Slope form of an equation that passes through the point (-1, 5) and has a slope of -2? y - 5 = -2(x- -1) y - 5 = -2(x + 1) Ax + By = C y = mx + b y - y 1 = m(x - x 1 ) 4

5 EQ: How do we write equations in point-slope form? What is the Point-Slope form of an equation that passes through the point (-1, 5) and has a slope of -2? y - 5 = -2(x- -1) y - 5 = -2(x + 1) It is easier to use point slope form of an equation to get to slope-intercept than to use the method we used over the weekend! All you have to do is simplify and solve for y... y - 5 = -2(x +1) y - 5 = -2x y = -2x + 3 5

6 EQ: How do we write equations in point-slope form? What is the point-slope form of the equation of a line that passes through the point (4, 6) and has a slope of 5? y - 6 = 5(x - 4) Change the equation above to slope-intercept form... y - 6 = 5x y = 5x -14 What is the point-slope form of the equation of a line that passes through the point (-1, 4) and has a slope of -2? y - 4 = -2(x + 1) Change this to Standard Form (Ax + By = C...) =y - 4 = -2x y = -2x x +2x 2x + y = 2 6

7 EQ: How do we write equations in point-slope form? (5, 3) m = 1 / 2 Point-Slope Form y + 3 = 1 (x -5) 2 y - 1/2 x = /2x - y = 5.5 1/2 x - y = 0.5 x + 2y = -5.5 x - 2y = -1 1/2x - y =-1/2 1/2x + y = 5.5 x - 2y = 1 x + 2y = -11 x + 2y = -6.5 x - 2y = 11 x - 2y = -o.5 Standard Form 7

8 EQ: How do we write equations in point-slope form? (1, 4), m = 5 2 Point Slope y + 4 = 5 ( x 1) 2 Standard 5x + 2y = 3 8

9 EQ: How do we write equations in point-slope form? Homework: pg #15 54 (multiples of 3), #55 57 all, #66 9

10 Algebra Tuesday December 7, 2010 EQ: Review point-slope and Chapter 1 and Chapter 3 In class today complete Lesson 5-5 In the Extra Practice Chapter 1 Standardized Test Practice Chapter 3 Standardized Test Practice All in the textbook! 10

11 Algebra Wednesday December 8, 2010 EQ: How do we know that two graphs are parallel or perpendicular to one another? Review Yesterday! Lesson 5-5 In the Extra Practice Chapter 1 Standardized Test Practice Chapter 3 Standardized Test Practice New Lesson 11

12 EQ: How do we know that two graphs are parallel or perpendicular to one another? Graph on the same graph, the two equations given: y = -2x + 4 y = -2x - 3 The lines are parallel. If they have the same slope, they will be parallel. What is the equation of a line that is parallel to y = 3x + 4 and passes through the point ( 1,2)? Write in slope intercept form. We are looking for a line that has a slope of 3 and passes through ( 1,2) Works just like yesterday! 12

13 EQ: How do we know that two graphs are parallel or perpendicular to one another? two line will be perpendicular to one another if their slopes are opposite, reciprocals or one another. Slope of 2 will be perpendicular to a slope of will be perpendicular to To get a slope that is perpendicular, take the opposite sign flip the fraction What is the equation of a line that is perpendicular to y = 2 x and passes through point (4,5)? Write in standard form. We are looking for a line that has a slope of 3/2 and passes through the point (4,5). Same as yesterday. 13

14 EQ: How do we know that two graphs are parallel or perpendicular to one another? Homework: December 8, 2010 on the syllabus! 14

15 Algebra Thursday December 9, 2010 EQ: How do we find the equation of a line that is parallel or perpendicular to another line? 15

16 EQ: How do we find the equation of a line that is parallel or perpendicular to another line? 16

17 EQ: How do we find the equation of a line that is parallel or perpendicular to another line? 17

18 EQ: How do we find the equation of a line that is parallel or perpendicular to another line? 18

19 EQ: How do we find the equation of a line that is parallel or perpendicular to another line? Find a line that is PARALLEL to... and passes through... Write your equation in STANDARD FORM (3,2) y = x ( 2,2) 2. ( 2, 5) y = 4x (4, 6) y = 3 / 4 x (5, 4) y = 2 / 5 x 2 5. (12, 3) y= 4 / 3 x (3, 1) 2x + y = 5 7. ( 3, 4) 3y = 2x 3 8. ( 1, 2) 3x y = 5 9. ( 8, 2) 5x 4y = ( 1, 4) 9x + 3y = 8 19

20 Find a line that is PERPENDICULAR to... and passes through... Write your equation in STANDARD FORM ( 2,2) y = 1/3x ( 6, 5) x y =5 Textbook! Lesson 5 6 pg. 832 #1 12 Write in slope intercept and standard form ( 4, 3) 4x + y = (0, 1) x + 5y = ( 2, 4) x 6y =2 16. ( 1, 7) 3x + 12y = ( 4, 1) 4x +7y = (10, 5) 5x + 4y = (4, 5) 2x 5y = (1, 1) 3x + 2y = 7 20