slope

SLOPE

SLOPESlope is the “tilt” of the line.Slope is the “slant” of the line.

Positive slope

Positive correlationNegative slope

Negative correlation

zero slope

undefined slope

SLOPE Slope is the steepness of the “slant” of the line. Slope is the steepness of a mountain side. Slope is the steepness of a wheelchair ramp. Slope is the steepness of a flight of stairs. Slope is the steepness of a plane’s decent. Slope is the steepness of a ski run. Slope is steepness of a skate board ramp.

SLOPEThese different slopes can be measured and

represented mathematically with a ratio. This ratio can be found by going from one

point on the line to another point by counting the vertical change and the horizontal change.

This ratio or slope is sometimes called the rise (vertical change) over the run (horizontal change).

Let’s investigate the steepness of this mountain slope.

#1) Pick two points on the side of the mountain.#2) Draw an imaginary grid.

#3) Count vertically and then horizontally from one point to the other.

vertically 12345horizontally

123 Slope =53

SLOPEThere are different names for the slope ratio.

vertical change 5horizontal change

3

Slope =53

rise run

5

3change in y

change in x

5

3

=

=

=

Let’s look at the “sign” of the slope or the correlation.

Slope =53

positive slope

Slope =53

-

“Going up the mountain.”

“Going down the mountain.”

negative slope

Counting Slope Positive Slope

Counting up … rise and right … run

Counting down… rise and left … run

+ / + = +- / - = +

Negative SlopeCounting up … rise and left … run

Counting down… rise and right … run

+/ - = -- / + = -

(2, 4)

(-3, 1)x

y

Finding slope on the coordinate plane.

1) Plot points

2) Draw line

3) Count - - vertically4) Count - - horizontally5) Write slope - as a ratio

+3

+5

Slope =35

+

(5, -2)

(-1, 2)

x

y

Finding slope on the coordinate plane.

1) Plot points

2) Draw line

3) Count - - vertically4) Count - - horizontally5) Write slope - as a ratio

+4

-6

Slope =+4-6

=-2 3

Find slope algebraically when given two points

my y

x x

( )

( )2 1

2 1

Point 1: (x1, y1) Point 2: (x2, y2)

Slope =difference between the y coordinatesdifference between the x coordinates

Find slope algebraically when given two points

Point 1: (-1, 2) Point 2: (5, -2)

Slope =difference between the y coordinatesdifference between the x coordinates

m =-2 - 2 5 - -1

- 4 6

- 2 3

= =

Example 1:

Find the slope of the line containing the points (6, 7) and (8, 3)

Remember each ordered pair is (x, y)Write slope formulaSubstitute into slope formula

Subtract the y coordinatesSubtract the x coordinates

m

( )

( )

7 3

6 8

m ( )

( )

4

2

m = -2

Example 2: Find the slope of a line containing (-

3, 6) and (-12, -9)

m

( )

( )

6 9

3 12

m ( )

( )

15

9

m 5

3

my y

x x

( )

( )2 1

2 1

(-3, 2)

(-4, -2)

x

y

Example 3: Through the given point, (-4, -2), graph the line with a slope of 4.

1) Plot point

2) Count slope

a) Count - - vertically

b) Count - - horizontally

5) Plot new . point

+4

+1

m =41

+

6) Draw line

The end