Rate of Changeand

Slope

Monday, November 1, 2010

Definition

• Rate of change allows you to see the relationship between two quantities that are changing.

Formula

Rate of change =

Finding the Rate of Change Using a Table

Cost of Renting a Computer

Number of Days

Rental Charge

1 $60

2 $75

3 $90

4 $105

5 $120

Rate of change =

The rate of change is $15 per day after the first day of rental.

Finding Rate of Change Using a Graph

• Rate of change =

• Use two points

• Divide

• Simplify

Slope Formula

• Slope = =

where x2 – x1 0

Find Slope Using Two Points

• Slope =

• Find the slope of the line through A(-2, 1) and B (5, 7).

• the slope of Line AB is

Find the slope of the line through each pair of points.

• C (2, 5) and D (4, 7)– Slope is 1.

• P (-1, 4) and Q (3, -2)– Slope is

Horizontal and Vertical Lines

• Slope =

• Substitute two points

• The slope of a horizontal line is 0.

• Slope =

• Substitute two points

• The slope of the vertical line is undefined.

Find the slope of the line.

Slope = 0

Find the slope of the line.

Slope = undefined

Find the slope of the line.

Slope = undefined

Find the slope of the line.

Slope = 0

Closure

• What are two ways to find the slope of a line?– You can count the units of rise and run between

two points on graph. Or you can find the difference of the y-coordinates, and, in the same order, the difference of the x-coordinates. Then write the quotient of the difference of the y-coordinates divided by the difference of the x-coordinates.