Slope of Lines

Sec: 3-3Sol: G.2d

http://www.youtube.com/watch?v=C1shoHMadzw&feature=related

Slope

Definition: denoted m, it is the vertical change (y the rise) over the horizontal change(x the run).

We use the first equation when given a graph, the second when given two points.

run

risem

12

12

xx

yym

Find the Slope of the line.

Find the slope of the line passing through the points

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

Try these:1. (0, 3)(4, 8)2. (-5, 1)(5, -4)3. (-3, -2)(6, 1)

Classification of lines by slope

Negative slope Positive

slope

UndefinedSlope

ZeroSlope

Parallel lines: Are two lines in a plane that do not intersect. Two lines are parallel IFF (if and only if) they have the same slope. m1=m2

Perpendicular lines: Two lines in a plane the intersect to form a right angle.Two lines are perpendicular IFF their slopes are negative reciprocals of each other.

or2

1

1

mm 121 mm

Ex:

• Given P(-2, 2), Q(2, 1), R(1, -1), and S(5, -2), determine if is parallel to or perpendicular to .

PQRS

Example

Graph the line that passes through the point (3, 5) that is perpendicular to TK with T(0, 2) and K(5, 0).

Rate of Change

Is a comparison of how much one quantity changes, on average, relative to the change in another quantity.

change Horizontal

change Verticalchange of Rate

0

1000

2000

60 120 180

(60,1000)

(180,0)

(0,2000)

18060

01000

Roc

3

18

120

1000

Roc

Because the line goes down it is descending 8(1/3) ft/sec

Assignments

Classwork: WorkbookHomework: pg 142 – 143 16 – 38 even 44-46