algebra 4.4 slope. finding slope m = slope = rise run = change in y change in x y 2 – y 1 = x 2...

Algebra

4.4 Slope

Finding Slope

m = slope

= rise

run

= change in y

change in x

y2 – y1=

x2 – x1

x

y

..

(x1 , y1)

(x2 , y2)

The order the arcs subtract does not matter, as long as the order is the same for both!

Find the slope of the line.

4 – 2=

3 – (-2)x

y ..(-2 , 2)

(3 , 4)

y2 – y1=

x2 – x1

slope

2=

3 + 2

2=

5 The slope of the line is 2/5.

You try! Find the slope of the line.

1 – (-5)=

-2 – 1x

y

.

.(-2 , 1)

(1 , -5)

y2 – y1=

x2 – x1

slope

1 + 5=

-3

=

-3 The slope of the line is -2.6

Can you simplify slope? Yes!

Try another. Find the slope of the line.

2 – 2=

3 – (-1)x

y

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

y2 – y1=

x2 – x1

slope

0=

3 + 1

=

4 The slope of the line is 0.0

All horizontal lines have a zero slope.

It’s like jogging on flat ground, your slope is zero.

How about the slope between (2, 1) and (2, 4)?

4 – 1=

2 - 2

y2 – y1=

x2 – x1

slope

3=

0The slope of the line is undefined.All vertical lines have an undefined slope.

It’s like going up in an elevator, your rise can beanything, but your run is zero.

x

y

.

.(2 , 1)

(2 , 4)

Every type of slope.Positive SlopeGreater than 1

Uphill

Steep

Positive SlopeLess than 1

Uphill

Flatter

Negative SlopeGreater than 1

Downhill

Steep

Negative SlopeLess than 1

Downhill

Flatter

Slope = 0

Undefined Slope

Running up the hill is undefined!

Identifying a Slope of -3.

Is it uphill or downhill?

Downhill

Is it steep or flatter?

Steep

Rise -3

Run 1

Identifying a Slope of 1/4.

Is it uphill or downhill?

Uphill

Is it steep or flatter?

Flatter

Rise 1

Run 4

Identifying a Slope of -2/3.

Is it uphill or downhill?

Downhill

Is it steep or flatter?

Flatter

Rise -2

Run 3

Find the value of y so that the line passing through the points (-2, 1) and (4, y) and has a slope of 2/3.

y – 1=

4 – (-2)

y2 – y1=

x2 – x1

slope

y - 1=

6

= y - 1

32

32 Clear the fraction by multiplying by the LCD66

4= y 5

Find the value of y so that the line passing through the points (3, y) and (5, 8) and has a slope of 2.

8 – y=

5 – 3

y2 – y1=

x2 – x1

slope

8 - y=

2

= 8 - y

2

2 Multiply each side by 2.22

4= - y -4 = y 4

Homework

P. 230 #13 -19 Odd (graph, no graph paper required)

# 21 - 41 Odd (calculate, do not graph)