SlopeSlope

Slope describes the slant and direction of a line.

The slope of a line refers to the steepness of the line.

The slope also determines whether the linear function will

increase or decrease from left to right.

Slope measures the steepness of a line and is given by the formula:

rise

runslope =

x

y

O

run

rise

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

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

slope 12

12

mxx

yym

The subscripts indicate that you have a "first" point and a "second" point . 

Slope is sometimes referred to as "rise over run“. The 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).

Alien Explanation!

The slope is looked at as a fraction that represents

m =the change in the y direction

the change in the x directionThe variable used to represent slope is m.If the slope ends up as a fraction, LEAVE it as a fraction in simplest form. Do not change it to a decimal!

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

3

2

3

2

1X 1Y

2X 2Y

12

12

xx

yym

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

)2(4

55

m6

10

3

5

12

12

xx

yym

1X 1Y 2X 2Y

12

12

xx

yym

)3()5(

)6()2(

m8

4

2

1

1X 1Y 2X 2Y

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 horizontals lines are of the form: y = “a number“ (ex. y = 4)

Now 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 are of the form x = “a number“ (ex. x = 4). 

)5()5(

)4()2(

m0

2

This slope is undefined.

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)

(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

If I am given a line, how do I find the slope?

Pick any two points on the line and use the slope formula.

If I pick two different points than someone else won’t I get a different answer for the slope?

No, the math will be different, but the answer will be the same.

If the slope ends up positive, what will the line look like?

If the slope ends up negative, what will the line look like?

The slope formula

12

12

xx

yym