Bellwork 4.3a SLOPE CONJECTURE Objectives: 1. Define the slope of a line 2. Discover formula for finding the slope of a line.

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Presentation transcript:

Bellwork

4.3a SLOPE CONJECTURE Objectives: 1. Define the slope of a line 2. Discover formula for finding the slope of a line.

Slope Slope means rise over run rise run Slope is how much a line rises compared to how much it runs.

Slope Think of some activities or structures that involve the word slope. Skiing, Stairway, etc..

Notice the Stair Step effect Slope is how much a line rises compared to how much it runs This line rises 1 and runs -1 Slope = rise run = 1 -1

The Slope Formula Any two points on a line can be labeled (x 1,y 1 ) and (x 2,y 2 ) so...

The Slope Formula The formula is:

Label the 2 Points (-1,5)=(x 1,y 1 ) (2,2)=(x 2,y 2 )

Using the Formula Let (-1,5) be (x 1,y 1 ) and (2,2) be (x 2,y 2 ) so… 2-5 = -3 =

So..The slope is -1 Slope = -1

Notice the Stair Step effect Slope = -1

Calculate the slope of this line. (0,0) (5,2)

Calculate the slope of this line. (0,0) (5,2) (x 1, y 1 ) (x 2, y 2 )

(x 1, y 1 ) (5,2)(0,0)

The slope is: (0,0) (5,2) Go up 2. Go right 5.

Calculate the slope of this line. (-3,-4) (-5,3)

(x 2, y 2 )(x 1, y 1 ) (-3,-4) (-5,3)

Positive and Negative Slopes Lines with negative slopes go down (decrease) from left to right.

This line goes down from left to right. m = (-3,-4) (-5,3)

Positive and Negative Slopes Lines with positive slopes go up (increase) from left to right.

This line increases from left to right. m = (0,0) (5,2)

Horizontal and Vertical Lines Horizontal lines have a slope of 0. Vertical lines have NO Slope

Horizontal Lines Slope = 0

Vertical Lines No Slope

Classwork -page 190 #’s 1-4; 12-23; 25-27