Chapter 2 Lines.

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Presentation transcript:

Chapter 2 Lines

2.1 Lines in Space Graphing Lines

y 8 7 6 5 ● (3 , 4) 4 3 2 ● (-8 , 1) 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 Origin -1 -2 -3 -4 ● -5 (-2 , -5) -6 -7

y 8 7 y = 2x + 3 6 5 4 3 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7

y = 2x + 3 x y 3 ( 0 , 3)

y 8 7 y = 2x + 3 6 5 4 ● 3 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7

y = 2x + 3 x y 3 ( 0 , 3) 2 7 ( 2 , 7)

y 8 ● 7 y = 2x + 3 6 5 4 ● 3 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7

y 8 7 y = -3x + 8 6 5 4 3 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7

y = -3x + 8 x y 2 2 ( 2 , 2)

y 8 7 y = -3x + 8 6 5 4 3 ● 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7

y = -3x + 8 x y 2 2 ( 2 , 2) 5 -7 ( 5 , -7)

y 8 7 y = -3x + 8 6 5 4 3 ● 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 ● -7

2.1 Lines in Space Graphing Lines Intersection of two lines

● ● ● ● (1 , 5) y 8 y = 2x + 3 7 y = -3x + 8 6 5 4 3 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 ● -7

y 8 7 y = 3x – 6 6 5 4 3 2 1 ● X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 ● -3 -4 -5 ● -6 -7

● ● ● y 8 y = -2x + 9 7 y = 3x – 6 6 5 4 3 (3 , 3) 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7

Problem Solving with Lines Wade and Brent are in a race. Wade is extremely confident and gives Brent a 20 meter head start. The race is 100 meters. Wade can run 8 meters per second. Brent can run 6 meters per second. Who will win the race? By how much?

meters ● (10, 80) ● ● ● ● ● ● ● ● seconds

2.2 Equations of Lines

y 8 7 y = 2x + 3 6 ● 5 4 ● 3 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7

y 8 7 y = -3 x + 5 6 2 ● 5 4 3 ● 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7

y 8 7 6 ● 5 4 ● 3 2 ● 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7

y 8 7 6 5 ● 4 3 2 ● 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 ● -2 -3 -4 -5 -6 -7

y 8 ● 7 6 5 4 3 ● 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 Origin -1 -2 -3 -4 -5 -6 -7

y 8 7 6 5 ● 4 3 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 Origin -1 -2 -3 -4 -5 -6 ● -7

y 8 7 6 5 4 3 ● 2 1 ● X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 Origin -1 -2 -3 -4 -5 -6 -7

2.3 Parallel and Perpendicular Lines

y 8 7 6 5 ● 4 ● 3 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 Origin ● -1 -2 -3 -4 -5 -6 -7

y 8 7 6 5 4 3 ● 2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 Origin -1 -2 -3 -4 ● -5 ● -6 -7