4.4 Slope Formula

Slope can be expressed different ways:

A line has a positive slope if it is going uphill from left to right.

A line has a negative slope if it isgoing downhill from left to right.

2 1

2 1

( ) vertical change

( ) horizontal change

y y risem

x x run

UP or DOWN RIGHT

Rise

3

4

Run

THE SLOPE IS

34

Find the slope of the following line.

The slope is…

1

2

Find the slope of the line.

The slope is….

-3

When given the graph, it is easier to apply “rise over run”.

1) Determine the slope of the line.

Determine the slope of the line shown.

rise

run

2

1 2

What is the slope of a horizontal line?

The line doesn’t rise!

m 0

number0

All horizontal lines have a slope of 0.

What is the slope of a vertical line?

The line doesn’t run!

All vertical lines have an undefined slope.

m number

0undefined

Find the slope of these lines.

• Black line 3

• Red Line 1

• Blue Line -1/2

Find the slope of these lines

• Orange line = 0

• Green Line = Undefined

Determining Slope

Rise=1

Slope= 12

Slope=3

Rise=6Run =2

Run =2Rise=12Run =4

Let’s find the slope of a line with two points, WITHOUT LOOKING AT A GRAPH.

REMEMBER THE SLOPE FORMULA???!!!!!

2) Find the slope of the line that passes through the points (-2, -2) and (4, 1).

(1 ( 2))

(4 ( 2))m

2 1

2 1

( )

( )

y ym

x x

(1 2)

(4 2)

When given points, it is easier to use the formula!

y2 is the y coordinate of the 2nd ordered pair (y2 = 1)

y1 is the y coordinate of the 1st ordered pair (y1 = -2)

13

6 2

3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).

m y2 y1

x2 x1

1 3

2 ( 5)m

1 3

2 5m

2

7m

x1 y1 x2 y2

Sample Problems:• Find the slope of the line thru the points given:

(-3,-1) and (-2,4)

(-3,4) and (2,-2)

x1 y1 x2 y2

x1 y1 x2 y2

Independent Practice: Calculate the slope for each pair of points. Classify each slope as positive, negative, zero, or undefined.

1. (2, 2) and (3, 5) 2. (0, 0) and (3, 0)

3. (-2, -1) and (-1, -4)

4. (2, 3) and (2, 7)

5. (-1, -1) and (5, 5)

6. (8, 4) and (6, 4)

Slope: 3 Classification: Positive

Slope: -3

Classification: Negative

Slope: 1 Classification: Positive

Slope: 0 Classification: Zero

Slope: Undefined Classification: Vertical

Slope: 0

Classification: Horizontal

1

Draw a line through the point (2,0) that has a slope of 3.

1. Graph the ordered pair (2, 0).

2. From (2, 0), apply rise over run (write 3 as a fraction).

3. Plot a point at this location.

4. Draw a straight line through the points.

3

If you know the slope and one point on the line you can draw the line.

Example: slope is 1/3 and the point (-2,-1)

Now you draw a line.

• Given: slope is 2/3 and the point is (1,0)

• Given: slope is –3 and the point is (–2,4)

• Given: slope is 1 and the point is (2,3)

Graph the line y = 3x +1,then tell me the slope of that line

after you graphed it.The slope is 3

x y

-2

-1

0

1

2

-5

-2

1

4

7

Graph the line 2x + y = 4,then tell me the slope of that line

after you graphed it.

x y

-2

-1

0

1

2

8

6

4

2

0

The slope is -2y = -2x + 4

Graph the line y = -5,then tell me the slope of that line

after you graphed it.

x y

-2

-1

0

1

2

-5

-5

-5

-5

-5

The slope is 0

Graph the line y = 2x,then tell me the slope of that line

after you graphed it.

x y

-2

-1

0

1

2

-4

-2

0

2

4

The slope is 2

Graph the line y = 3x - 2,then tell me the slope of that line

after you graphed it.

x y

-2

-1

0

1

2

-8

-5

-2

1

4

The slope is 3

Graph the line 2x + 3y = 6,then tell me the slope of that line

after you graphed it.

x y

-6

-3

0

3

6

6

4

2

0

-2

The slope is -2/3

Graph the line y = -x - 2,then tell me the slope of that line

after you graphed it.

x y

-2

-1

0

1

2

0

-1

-2

-3

-4

The slope is -1

Graph the line 3x – 4y = 12,then tell me the slope of that line

after you graphed it.

x y

-8

-4

0

4

8

-9

-6

-3

0

3

The slope is 3/4

Graph the line x – y = 5,then tell me the slope of that line

after you graphed it.

x y

-2

-1

0

1

2

-7

-6

-5

-4

-3

The slope is 1y = x - 5

The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r.

To solve this, plug the given information into the formula

2 64

4 r

4 4

1 4 r

To solve for r, simplify and write as a proportion.

4 4

1 4 r

2 6

44 r

Cross multiply.

1(-4) = 4(4 – r)

Simplify and solve the equation.1(-4) = 4(4 – r)

-4 = 16 – 4r-16 -16

-20 = -4r-4 -45 = r

The ordered pairs are (5, 6) and (4, 2)