Algebra ppt

[object Object],[object Object],The Slope Ratio

[object Object],[object Object],Real Life Examples Vertical Rise = 40 ft Horizontal Run = 200 ft m= vertical/horizontal m= 40/200 = 1/5

[object Object],The Slope of a Line m= rise run = change in y change in x y₂-y₁ = x₂-x₁ ,[object Object]

[object Object],[object Object],Positive Slope y₂-y₁ x₂-x₁ m= = 4-0 3-1 = 2 4 = 2 There is a positive slope of 2 therefore the line rises from left to right.

Negative Slope Let (x₁, y₁)= (0,3) and (x₂,y₂)=(4,1) Find m. y₂-y₁ x₂-x₁ m= = 1-3 4-0 = 4 -2 = -1 There is a negative slope of -1/2 therefore the line falls from left to right. 2

Zero Slope ,[object Object],[object Object],y₂-y₁ x₂-x₁ m= = 2-2 4-1 = 3 0 = 0 There is a zero slope therefore the line is horizontal. We can compare this to walking across the floor.

Undefined Slope ,[object Object],[object Object],y₂-y₁ x₂-x₁ m= = 3-⁻1 5-5 = 0 4 = Undefined! The slope is undefined because division by 0 is undefined and the expression 4/0 has no meaning. This line is vertical and we can compare it to walking up a wall, impossible.

Summary: Slope of Lines Positive- rises left to right Negative- falls left to right Zero- horizontal Undefined- vertical

[object Object],[object Object],[object Object],Slope Intercept Form of a Line

Example ,[object Object],3x + 5y −15 = 0 y= x+ 3 -3 5 Solve for y by subtracting 5y from both side and then divinding both sides by -5. slope y-intercept

[object Object],Ladder rise 12 run 5 = 12ft 5ft

Making Sense of Slope! A D C B E Choose different pairs of points on the line and find their slope. What do you notice? What conclusion can you draw?

Making Sense of Slope! Anwsers mAB= mBC= mCD= mDE= 1 2 1 2 1 2 1 2 Now, based on the conclusion that the slope is ½ between each set of points, complete the sentence: No matter what pair of points you choose on a line, the ______ remains constant. *slope

The Slope of the Road The slope of the road is the vertical rise divided by the horizontal run. If the vertical rise is 24 feet for a horizontal run of 1 mile, determine the slope of the road. *Hint- 1 mile=5280 feet 24ft 24ft 1 1mi 5280ft 220 = = *This means that for every 1ft that you move up, you also move 220ft forward.

CREDITS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Algebra ppt

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Algebra ppt