NOTIONS OF SLOPE

WHAT IS SLOPE?

Slope is typically represented by m The y intercept is represented by b

m = y / x

m = rise/run

m= (y2 – y1) / (x2 – x1)

slope intercept form: y=mx + b

Slope is the constant rate of change ( )per unit

NOW, LET’S EXPLORE SLOPE GRAPHICALLY.

1)Open a new GeoGebra file

2) Create two points on your graph.

3) Create a line through those two points.

Discussion

MISCONCEPTIONS OF SLOPE

A fraction always gives a wider slope (a slope that is less steep)

Truth: a fraction with a larger numerator than denominator will result in a steeper slope EXAMPLE: 15/3 will be steeper than 3/15

The placement of y and x in the equationWe tend to put x on the top of the

fraction because we are used to x coming before y

NOT CORRECT: X2 – X1 CORRECT: Y2 – Y1

Y2 – Y1 X2 – X1

LET’S EXPLORE A REAL WORLD APPLICATION

Discussion

ARE THERE ANY QUESTIONS?

COMMON SLOPE FORMULAS

HORIZONTAL LINE: m = 0

VERTICAL LINE: m = undefined

LINE THAT FALLS TO THE RIGHT:

m = negative \

LINE THAT RISES TO THE RIGHT:

m = positive /

NOTIONS OF SLOPE

DAY 2

LESSON INSTRUCTIONS

Open a new Geogebra file Access the internet to locate a picture of

bellbottom jeans Save the file to pictures Import the picture to Geogebra and

position the picture on the grid Plot two points on the picture, one on the

outer part of the jeans at the knee, and the second on the outer part of the jeans at the ankle.

Find the slope of the line that these two points would create.

Discussion