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Algebra II Chapter 2 section 2 Lets get linear. For a function to be linear In a table, differences between ranges the same as long as differences between.

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Presentation on theme: "Algebra II Chapter 2 section 2 Lets get linear. For a function to be linear In a table, differences between ranges the same as long as differences between."— Presentation transcript:

1 Algebra II Chapter 2 section 2 Lets get linear

2 For a function to be linear In a table, differences between ranges the same as long as differences between domains the same In a graph, forms a line In an equation: 1. No exponents on variables 2. No variables times variables 3. No variables on bottom of fractions

3 Slope Rise over run Y 2 -Y 1 X 2 -X 1

4 Find the slope 1. (3,4) (2,6) 2. (5,-2) (8,12) 3. (-8, 10) (16, -2)

5 Slope intercept form Y = mX + b Slope Y- intercept

6 Name the slope and one point on the line Y = 1/3 X -4 Slope = 1/3Point (0,-4)

7 Point slope form (y - y 1 ) = m (x - x 1 ) Slope Y of one pointX of one point

8 Find the equation of a line in point slope form Slope = 2 & goes through point (5,6) (y - 6) = 2 (x - 5) (y - y1) = m (x - x1)

9 Convert point slope to slope intercept (y - 6) = 2 (x - 5) Distribute the slope y - 6 = 2x - 10 Add y 1 to both sides y = 2x - 4

10 Find the equation of the line in slope intercept form 1. Slope 3 & goes through ( 5,1) 2. Slope ½ & goes through (-2,4) 3. Goes through (3,1) and (-2,5)

11 Finding intercepts given slope intercept Y = mX + b b is the y-intercept

12 Y = mX + b If y = 0 0 = mX + b -b = mX -b = X m X-intercept means Y = 0

13 Find the x, y intercept and the slope 1. Y= 3X Y = ½ X Y = 3X + 10

14 Parallel Lines Parallel lines have the same slope Find the slope of a line parallel to y = x The slope is 3

15 Equations of parallel lines Find the equation of a line parallel to y = 2x + 5 that goes through (-1,4) (y - y 1 ) = m(x - x 1 ) (y - y 1 ) = 2(x - x 1 ) (y - 4) = 2(x + 1)

16 U - Try 1. Parallel to y =-2x + 6 through point ( 4,9 ) 2. Parallel to y = 1/2x + 4 through point ( 3,2 ) 3. Parallel to y = 22x + 7 through point ( 1,-2 )

17 Perpendicular lines Perpendicular lines have slopes that are opposite reciprocals of each other

18 Perpendicular lines Find the slope of a line perpendicular to y = x Reciprocal of 2 = 1/2 Opposite Reciprocal of 2 = -1/2

19 Find the equation of a line perpendicular to y = -1/3x + 5 and goes through ( 4,5) Slope = 3 (y - y 1 ) = m ( x - x 1 ) (y - y 1 ) = 3 ( x - x 1 ) (y - 5) = 3 ( x - 4)

20 U - Try 1. perpendicular to y = -2/3x + 7 and goes through ( 3, 4) 2. perpendicular to y = -4x + 25 and goes through ( -2, 1) 3. perpendicular to y = -x +.2 and goes through ( ½, 5 )


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