SLOPE OF A LINE

8.F.2 COMPARE PROPERTIES OF TWO FUNCTIONS EACH REPRESENTED IN A

DIFFERENT WAY (ALGEBRAICALLY, GRAPHICALLY, NUMERICALLY IN TABLES, OR

BY VERBAL DESCRIPTIONS).

SLOPE

Slope describes the slant or direction of a line.

Given two points (x1, y1) and (x2, y2),

the formula to find the slope of the straight line going through these two points is:

slope 12

12

mxx

yym

SLOPE

•The subscripts in each ordered pair indicate that one is a "first" point and the other is a "second" point . 

SLOPE

•Slope also called “rate of change” and sometimes referred to as “rise over run“.

•The slope fraction consists of the "rise" (change in y, going up or down) divided by the "run" (change in x, going to the left or right).

The two points shown are: (0, -4) and (-3, -6). Now we have two points we can put them in the slope formula:

0-3-

)4(6 m

3

2

3

2

1X 1Y

2X 2Y

12

12

xx

yym

EXAMPLE #2

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

)2(4

55

m6

10

3

5

12

12

xx

yym

1X 1Y 2X 2Y

FIND THE SLOPE: (-3, 6) AND (5, 2)

12

12

xx

yym

)3()5(

)6()2(

m8

4

2

1

1X 1Y 2X 2Y

SLOPEThere are four possibilities for the

slope of a line:

Positive Slope

x

y

m > 0

Line rises from left to right.

Negative Slope

x

y

m < 0

Line falls from left to right.

HORIZONTAL LINES

The points (-3, 4) and (5, 4), the slope is:

For every horizontal line, a slope of zero means the line is horizontal, and a horizontal line means you'll get a slope of zero. The equation of all horizontal lines is of the form y = “a number” (ex. y = 4)

VERTICAL LINESNow consider the vertical line of the equation x = 4:

A vertical line will have no slope, and “the slope is undefined" means that the line is vertical.  The equation of all vertical lines is of the form x = “a number” (ex. x = 4). 

SLOPEThe other two possibilities for the

slope of a line:Zero Slope

x

y

m = 0

Line is horizontal.

m is undefined

Undefined Slope

x

y

Line is vertical.

FIND THE SLOPE OF A LINE THAT CONTAINS POINTS: (5, 4) AND (5, 2).

12

12

xx

yym

)5()5(

)4()2(

m0

2

This slope is undefined.

FIND THE SLOPE

(5, -2)

(11, 2)

(3, 9)

12

12

xx

yym

311

92

mRed

511

)2(2

m

Blue

Green

8

7

3

2

2

11

1X 1Y

2X 2Y

1X 1Y

2X 2Y

1X 1Y

2X 2Y

Are we going too fast?Let’s review!

(run) Change Horizontal

(rise) Change Vertical Slope

slope. is steepness

describe to termalmathematic The

Q & A

If I am given a line on the coordinate plane, how do I find the slope?•Pick any two points on the line and use the slope formula

OR

•Find the “rise” (change along the y-axis) and the run (change along the x-axis.

Q & A

If I pick two different points than someone else won’t I get a different answer?•No, the math will be different, but the answer will be the same.

First pick any two points on the line.

Then find the coordinates of the points and use them in the slope formula.

(5,6)

(-4,-2)

y

x-20 -10 10 20

Graph the points (0, 400), (15, 250)

Does the direction of the line show a positive or negative trend?

500

1000

-500

-1000

KEY SKILLS

Negative.

Find the slope.

KEY SKILLS

Edgar deposited $100 in the bank. After 6 weeks he had deposited a total of $220. Graph the amount of money he has in his account, then find the slope.

What are the 2 sets of (x, y) coordinates?

TRY THIS

(0, 100) (6, 220)

y

x-10 -5 5 10

Graph the points (0, 100), (6, 220)

Does the direction of the line show a positive or negative trend?

125

250

-125

-250

KEY SKILLS

Positive.

Find the slope.

TRY THIS

KEY SKILL

.m = y2 – y1

x2 – x1

(0, 100) ( 6, 220)x1 y1 x2 y2

Label the coordinates

Substitute into the formula

m = 220 – 100

6 - 0=

1206

= 20

The slope = 20