Slope of a LineThinker

See if you can tell me the four types of slope and draw them!

Types of Slope

PositiveNegative

Zero

Undefinedor

No Slope

Common Core Objective # 30•Finding the AOC or SLOPE on a table or

graph.

Slope is the measure of the steepness of a line.

•

The letter “m” isused to represent

slope.

Why? Why not?

Slope of a line is its rate of change. Often the letter m is used. Change is often symbolized in mathematics by a delta for which the symbol is the Greek letter: Δ

If given 2 points on a line, you may findthe slope using theformula m = y2 – y1

x2 – x1

Find the slope of the line through the

points (3,7) and (5, 19).x1 y1 x2 y2

m = 19 – 7 5 – 3

m = 12 2 m = 6

(3, 4) and (-6, -2)m = -2 – 4 -6 – 3

m = -6 -9

m = ⅔

USING A TABLE

• How would one find the slope of this table?

• Find the change in y-values compared to the change in x-values.

• It has an AOC or SLOPE of 2

USING A TABLE

• Find the slope of this table.• It does not have one constant rate of

change but each interval has it’s on.• What could one have done to verify?• GRAPHING IS A POSSIBILITY

Another method to use when given a graph

Is RISE RUN

rise = 4

run = 5

m= rise runm= 4/5

SPECIAL CASES OF SLOPE

• HOW DO YOU GET ZERO OR UNDEFINED FROM A SET OF POINTS?

2 special cases of slopeGiven the points (5,4)

and (1,4), if you use the slope formula you will come out with

m = 0 -4 Or just 0 since it is the

numerator and 0 divided by –4 is ALWAYS 0

Given the points (4,2) and (4,9), if you use the slope formula you will come out with

m = 7 0However, 0 in the However, 0 in the

denominator denominator IS IS NOT 0 but NOT 0 but UNDEFINED!UNDEFINED!

Special Case SamplesM=0 M=Undefined

• 1.

Notebook Examples• Find the slope of the

line given two points or a graph:

• (1) (1, 2), (4, 8)• (2) (-5, 2), (1, -4)• (3) (7, 6), (3, 6)• (4) (2, 6), (8, 1)

•

• Answers• (1) m = 2• (2) m = -1• (3) m = 0• (4) m = -5/6• (5) Undefined• (6) m = -3/2

(6)

(5)

HOMEWORK• You will have a 10 question quiz –

1 point each Monday about the following three topics.

• (1) Slope-Intercept Form• (2) Standard Form of a line• (3) Point-Slope Form• Each has an equation and is used

for different purposes• You can use your notes