The Slope of a Line

Important things about slope…•Slope is the change in y over change in x.•Slope is represented by the letter m•Vertical line has NO slope•Horizontal line has a slope zero (0)

Formula for slope:

12

12

xxyym

runrise

xy

= =

Find the slope of a line passing through points (1,1)

and (3,-2)

3121

m

23

23

A slope of -3/2 means that or every time y goes down 3, x moves over 2

Graph and count to check.

1234

-4-3-2-1-4 -3 -2-1 1 2 3 4

Classify lines by their slope:

1. A line with a positive slope rises from left to right (m>0)

x

y

2. A line with a negative slope falls down from left to right

(m<0)

x

y

3. A line with a zero slope is horizontal (m=0) Equation y = 3

x

y

4. A line with an undefined slope is vertical (m is undefined) YOU

CANT DIVIDE BY 0!

x

y

RATE OF CHANGE: At 3:00 p.m. a car leaves the city. By 5:00 it has traveled 90 miles. Find its average speed.

Change in milesChange in time(hours) 35

090

mph45Notice you have two pairs:(3,0) and (5,90)

Where x is time and y is miles.

The temp. is 63 F at 7a.m. By 10a.m., its 45 F. Find the

average rate of change in temp.Change in temp

Change in time 1074563

318

= -6 degrees per hour

Two pairs:(7,63) and

(10,45)

Find the value of y for the line going through points (-3, -2), (1, y) when the slope of the

line is 22 = -2 – y -3 - 1

2 = -2 – y -4-8 = -2 - y

6 = y