Reminder We do not have class this Thursday (September 25). I will not be in my office during my...

Reminder

We do not have class this Thursday (September 25).

I will not be in my office during my regular office hours tomorrow (Sept 24).

Copyright © Houghton Mifflin Company. All rights reserved. 3 | 2

In the picture, the third step of the ladder is 3 feet above the ground.

3 ft

1 ft

It is also a horizontal distance of 1 foot from the base of the ladder.

The ladder meets the ceiling at a horizontal distance of 4½ feet from the base of the ladder,

? ftHow high is the ceiling?

4½ ft


3 ft

1 ft4½ ft

? ft

How high is the ceiling?

5.4

?

1

313.5


A fundamental property of lines is that the ratio of “rise” to “run” is the same no matter what two points on

the line are used.

rise

run

rise

run

riserun =

riserun


SLOPE


x

y

1 2 3 4 5 6 7 8 9

8

7

6

5

4

3

2

1

•

The slope of this line is

m = = 2.1

2

•rise

run

Slope is the ratio of rise to run between any two points.

Slope is a comparison ofrise (vertical change) torun (horizontal change) between points.

Slope = =

The letter m is usually used for slope.

rise

runy x


x

y

1 2 3 4 5 6 7 8 9

8

7

6

5

4

3

2

1

•

•

5

10

Here is the same line. What if we compute the slope using 2 other points on the line?

Slope =

rise

run

10

52


x

y

1 2 3 4 5 6 7 8 9

8

7

6

5

4

3

2

1

Slope is a measure of steepness of a line.

If slope (m) is – the lineis falling left to right.

The function is decreasing.

If slope (m) = 0, the line is horizontal.

For a vertical line, slope is not defined.

If slope (m) is + the lineis rising left to right.

The function is increasing.

m = +2

m = –1

m = 0


What is the slope of our ladder?

3 ft

1 ft

3


The slope of a line is the average rate of change of its height.

In other words, the slope of a line tells us the change in height (y) for each one unit change along the horizontal (x).

x

y

1 2 3 4 5 6 7 8 9

8

7

6

5

4

3

2

1


x

y

1 2 3 4 5 6 7 8 9

8

7

6

5

4

3

2

1

5

10

•

•(1, 5)

(–4, –5)

Slope =

y2 y1

x2 x1

Slope =

5 ( 5)

1 ( 4)

10

52

25

10

1)4(

5)5(


x

y

1 2 3 4 5 6 7 8 9

8

7

6

5

4

3

2

1

•

•

What is the slope of the line shown?

2

3(2,2)

(0,-1)02

)1(2

2

3=


x

y

1 2 3 4 5 6 7 8 9

8

7

6

5

4

3

2

1

•

•

What is the slope of the line shown?

4

5(0,2)

(4,-3) 40

)3(2

4

5

4

5

=

04

2)3(

4

5

4

5

=

vertical intercept

horizontal intercept

•


Computing slope:

Example 1: Find the slope of the line that passes through the points (5, 7) and (-3, 1).

Example 2: Find the slope of the line with horizontal intercept 5 and vertical intercept 2.

Example 3: Find the slope of the line that passes through the points (4, 5) and (9, 5).

Example 4: Find the slope of the line that passes through the points (-3, 2) and (-3, 9).


Computing slope:





¾


Computing slope:





¾

–2

..5


Computing slope:





¾

0 (the line is horizontal)

–2

..5


Computing slope:





¾

0 (the line is horizontal)

No Slope (the line is vertical)

–2

..5


x

y

1 2 3 4 5 6 7 8 9

8

7

6

5

4

3

2

1

On coordinate axes, draw a line whose slope is 2 and which has vertical intercept –7.

What is the horizontal intercept?


x

y

1 2 3 4 5 6 7 8 9

8

7

6

5

4

3

2

1

On coordinate axes, draw a line whose slope is –½ and which has horizontal intercept 3.


24 ft

Questions:

1. What is the slope of the roof?

2. What is the horizontal intercept of the roof?

?

12 ft

15 ft

Suppose we draw in an x and y-axis.

●

5 ft

3. If we move 5 feet to the right of center, how high is the roof?


Homework:

Read Section 3.1 (through middle of page 214)

1 # S-1, S-2, S-3, S-5, S-7, S-8

Pages 222 – 224 # 1 – 5, 7, 13

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