Assignment 8

course mth 163

郸葤牙`僲饰枛贤溸蕡溁╝ssignment #008

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

008.

Precalculus I

02-09-2007

......!!!!!!!!...................................

20:58:46

`q001. Note that this assignment has 4 questions

For the function y = 1.1 x + .8, what are the coordinates of the x = 2 and x = 9 points? What is the rise between these points and what is the run between these points? What therefore is the slope between these points?

......!!!!!!!!...................................

RESPONSE -->

Using substitution, we get (2, 3) and (9, 10.7)

y=1.1 (2) + .8 y = 1.1(9) + .8

y=2.2 + .8 y = 9.9 + .8

y= 3 y = 10.7

The rise is the the change in the y coordinate:

10.7 - 3 = 7.7

The run is the change in the x coordinate:

9 - 2 = 7

The slope is rise/run:

7.7 / 7 = 1.1

confidence assessment: 3

.................................................

......!!!!!!!!...................................

20:58:57

Evaluating y = 1.1 x +.8 for x = 2 and x = 9 we obtain y = 3 and y = 10.7. The graph points are therefore (2,3) and (9,10.7).

The rise between these points is 10.7 - 3 = 7.7 and the run is 9-2 = 7. Thus the slope is 7.7 / 7 = 1.1.

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

.................................................

......!!!!!!!!...................................

21:07:02

`q002. For the function y = 1.1 x + .8, what are the coordinates of the x = a point, in terms of the symbol a? What are the coordinates of the x = b point, in terms of the symbol b?

......!!!!!!!!...................................

RESPONSE -->

First substitute in:

then solve for a:

y = 1.1 a + .8

y - .8 = 1.1a

(y - .8) / 1.1 = a

Same thing for b:

y = 1.1 b + .8

y - .8 = 1.1b

(y - .8) / 1.1 = b

confidence assessment: 2

.................................................

......!!!!!!!!...................................

21:09:17

If x = a, then y = 1.1 x + .8 gives us y = 1.1 a + .8.

If x = b, then y = 1.1 x + .8 gives us y = 1.1 b + .8. Thus the coordinates of the x = a point are (a, 1.1 a + .8) and (b, 1.1 b + .8).

......!!!!!!!!...................................

RESPONSE -->

I made the question more complicated than it was. I understand where the y coordinates for each variable came from.

self critique assessment: 2

.................................................

......!!!!!!!!...................................

21:12:22

`q003. We see that the coordinates of the x = a point are (a, 1.1 a + .8) and (b, 1.1 b + .8). What therefore is the rise between these two points? What is the run between these two points?

......!!!!!!!!...................................

RESPONSE -->

The rise would be the change in the y coordinate:

(1.1b + .8) - (1.1a + .8)= 1.1b - 1.1a

The run is the change in the x coordinate:

(b - a)

confidence assessment: 2

.................................................

......!!!!!!!!...................................

21:12:36

The rise between the points is the rise from y = 1.1 a + .8 to y = 1.1 b + .8, a rise of

rise = (1.1 b + .8) -(1.1 a + .8) = 1.1 b + .8 - 1.1 a - .8 = 1.1 b - 1.1 a.

The run is from x = a to x = b, a run of

run = b - a.

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

.................................................

......!!!!!!!!...................................

21:15:53

`q004. We see that the rise between the x = a and x = b points of the graph of y = 1.1x +.8 is 1.1 b + .8 - (1.1 a + .8), while the run is b - a. What therefore is the average slope of the graph between these points? Simplify your answer.

......!!!!!!!!...................................

RESPONSE -->

Slope is the change in y / the change in x, so:

(1.1b - 1.1a) / (b - a)

1.1(b - a) / (b - a)

1.1

confidence assessment: 3

.................................................

......!!!!!!!!...................................

21:16:08

The slope is

slope = rise / run = (1.1 b - 1.1 a) / (b - a) = 1.1 (b - a) / (b - a) = 1.1.

The significance of this series of exercises is that the slope between any two points of the straight line y = 1.1 x + .8 must be 1.1, no matter whether the points are given by numbers (e.g., x = 2 and x = 9) or by symbols (x = a and x = b). Mostly

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

.................................................

Assignment 8

Good. Let me know if you have questions.