2.5 slope

Rate of change: Change in the dependent variableChange in the independent variable

The table shows the distance a band marches over time. Is the rate of change in distance with respect to time constant? What does the rate of change represent?

Time (min)

Distance(ft)

1 2602 5203 7804 1040

Distance marchedRate of change: Change in dependent

Change in independent= Change in distance

Change in time

520-260 2-1

= 260 1

780 - 5203-2

1040 - 7804-3

Rate of change=

Is the rate of change in distance with respect to time constant?

260 ft 1 min

What does the rate of change represent?

The distance the band marches per minute.

= 260 1

= 260 1

Slope: Vertical changeHorizontal change

= riserun

Find the slope of each line

Rise =run

1 Slope = 1 2

Rise =run

Slope = -2 3

-22 3

-5

0

5

-5 0 5

What is the slope of this line?

1. Find your two points on the line. (start at the point furthest to the left)

a. Do you go up or down to get to the next point?

a. If up—the slope is positive

b. If down—the slope is negative

Slope = -

2. Count how far you go up or down and that is the VERTICAL CHANGE

3. Count how far you go right and that is the HORIZONTAL CHANGE

32

Slope Formula: The slope of the line passing through point 1, (x1, y1), and point 2, (x2, y2) is

Examples:1. (1,7) and (6, 4)

2. (-4, -5) and (5, 6)

3. (-3, 2) and (4, -5)

slope = vertical change (rise)horizontal change (run)

change in change in

- x -x

2 1 y

xy y

2 1

4 7

6 1

= - 35

6 -5

5 -4= 11

9

-5 2

4 -3= -7

7= -1

(x1, y1) (x2, y2)

(x1, y1) (x2, y2)

Find the slope of each line

slope = vertical change (rise)horizontal change (run)

change in change in

- x -x

2 1 y

xy y

2 1

(-2,2) (4,2) (x1, y1) (x2, y2)

--

-2 24 -2

= 0 = 0

Slope of a horizontal line = 0

(-4,3)

(-4,-2)

(x1, y1)

(x2, y2) -2 3

-4 -4- = -5

Slope of a vertical line is undefined.

6 0

4 types of slopePositive Negative

Slope = ZeroSlope = Undefined

Horizontal line Vertical line

assignment

• Pg 43-47 1-20• Skip 2,4

• Note: for 3b and 6---pay attention to the change in units