Slope Lesson 4.6.

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Presentation transcript:

Slope Lesson 4.6

Change of y over the change of x Use m for slope Equation: 1 2 m = 2 1

m = ∆y ∆x ∆ Delta y over delta x ∆ delta means change Rise over run

Find the slope of a line given two points: (5, -2) (6, 3) 1 2 m = 2 1 3 - -2 6 - 5 5 1 = = 5

Four special slopes: Positive slope: m>0 Negative slope: m<0

Horizontal slope: m=0 Slope is zero Vertical slope: no slope undefined

Slope of parallel lines: Parallel lines have the same slope but different y-intercepts. Graph: y = 2x + 2 and y = 2x - 3 on the same graph.

= -1 Graph: y = x+3 and y = x -1 on the same graph.  Perpendicular lines: slopes are the opposite reciprocals of each other Their product equals -1. Graph: y = x+3 and y = x -1 on the same graph. = -1 

Show that CEF is a right triangle. What do I have to prove in order for it to be a right triangle? (Two sides slopes’ need to be opposite reciprocals in order to have a right angle.) 1. Slope of CE = 4 - 3 8 - 1 = 1 . 7 Since the slopes of FE & FC are opposite reciprocals, F is a right . Therefore, CEF is a right triangle. 2. Slope of FE = 7 - 4 4 - 8 = 3 . -4 3. Slope of FC = 3 - 7 1 - 4 = -4 . -3 = 4 3

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