Homework 23

#$&*

course Mth 158

11/4 8:09 pm

If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution:

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of

what you do or do not understand about it. This response should be given, based on the work you did in completing the

assignment, before you look at the given solution.

018. `* 18

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Question: * 2.3.34 / 30 (was 2.3.24). Slope 4/3, point (-3,2)

Give the three points you found on this line and explain how you obtained them.

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Your solution:

(-3,2) slope 4/3. Move 3 units in the x direction, 4 in the y direction to get (0,6)

(-3,2) slope 4/3 = -4/-3 so move -3 units in the x direction and -4 in the y direction to get (-6,-2)

From (0,6) with slope 4/3 we move 4 units in the y direction and 3 in the x direction to get (3,10).

The three points I found are

(-6,-2), (0,6), (3,10).

confidence rating #$&*: 3

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Given Solution:

* * STUDENT SOLUTION:

(-3,2) slope 4/3. Move 3 units in the x direction, 4 in the y direction to get

((-3+3), (2+4)), which simplifies to

(0,6)

(-3,2) slope 4/3 = -4/-3 so move -3 units in the x direction and -4 in the y direction to get

((-3-3), (2-4)) which simplifies to

(-6,-2)

From (0,6) with slope 4/3 we move 4 units in the y direction and 3 in the x direction to get

((0+3), (6+4)), which simplifies to

(3,10). The three points I obtained are

(-6,-2), (0,6), (3,10).

* 2.3.40 / 36 (was 2.3.30). Line thru (-1,1) and (2,2) **** Give the equation of the line and explain how you found the

equation.

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Your solution:

The slope is m = (y2 - y1) / (x2 - x1) = (2-1)/(2- -1) = 1/3.

Point-slope form gave me:

y - y1 = m (x - x1); using m = 1/3 and (x1, y1) = (-1, 1) we get

y - 1 = 1/3(x+1)

add 1 to both sides

y = 1/3 x + 3/3.

confidence rating #$&*: 3

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Given Solution:

* * STUDENT SOLUTION: The slope is m = (y2 - y1) / (x2 - x1) = (2-1)/(2- -1) = 1/3.

Point-slope form gives us

y - y1 = m (x - x1); using m = 1/3 and (x1, y1) = (-1, 1) we get

y-1=1/3(x+1), which can be solved for y to obtain

y = 1/3 x + 4/3.

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Self-critique (if necessary):

I am a bit confused about the solution. I got y + 1/3 + 3/3. Where is the 4/3 coming from??

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Self-critique Rating: 2

@&

I suspect you didn't fully multiply the (x + 1) by the 1/3. 1/3 ( x + 1 ) = 1/3 x + 1/3.

If you solve

y - 1 = 1/3(x+1)

for y you get

y - 1 = 1/3 x + 1/3 so that

y = 1/3 x + 1/3 + 1.

1/3 + 1 = 1/3 + 3/3 = 4/3, so we have

y = 1/3 x + 4/3.

*@

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Question: * 2.3.54 / 46 (was 2.3.40). x-int -4, y-int 4 * * ** What is the equation of the line through the given points

and how did you find the equation?

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Your solution:

First I had to find the two points.

The two points are (-4, 0) and (0,4).

Then I worked the problem for slope.

m = 4-0 / 0-(-4) = 4/4 which is 1.

substitute in for y=mx+b

y = x+4

confidence rating #$&*: 3

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Given Solution:

* * STUDENT SOLUTION: The two points are (0, 4) and (4, 0). The slope is therefore m=rise / run = (4-0)/(0+4) = 1.

The slope-intercept form is therefore y = m x + b = 1 x + 4, simplifying to

y=x+4.

STUDENT QUESTION

I obtained

-x + y = 4 or y = x + 4.

I followed the example in the book which leaves 2 solutions (example problem 2.3.51) Did I do it correctly?

INSTRUCTOR RESPONSE

Both your solutions represent the same line, and both are correct.

y = 1x + 4 means the same thing as y = x + 4; we rearrange this to -x + y = 4 (just subtract x from both sides).

-x + y = 4 is a 'standard form' of the equation of this line.

y = x + 4 is the 'slope-intercept' form of the equation.

You don't need to know this, but still another 'standard form' is obtained by subtracting 4 from both sides of the equation

-x + y = 4, giving us

-x + y - 4 = 0.

In this form we often want the coefficient of x to be positive, so we multiply both sides by -1 to get

x - y + 4 = 0.

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Self-critique (if necessary): OK

I see that I could have went a little further with this problem, even though I did come up with the correct solution.

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Self-critique Rating: 3

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Question: * 2.3.76 / 56 (was 2.4.48). y = 2x + 1/2. **** What are the slope and the y-intercept of your line and how did

you find them?

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Your solution:

This is already in y=mx+b format.

Therefore, the y-intercept is (0, 1/2).

The slope is m = 2.

confidence rating #$&*: 3

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Given Solution:

* * the y intercept occurs where x = 0, which happens when y = 2 (0) + 1/2 or y = 1/2. So the y-intercept is (0, 1/2).

The slope is m = 2.**

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Self-critique (if necessary): OK

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Self-critique Rating:

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Question: * 2.3.62 / 22 (was 2.4.18) Parallel to x - 2 y = -5 containing (0,0) **** Give your equation for the requested

line and explain how you obtained it.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

First I solved the equation for y.

x - 2 y = -5

I subtracted x from both sides.

-2y = -x - 5

Then I divided both sides by -2.

This gave me:

y = 1/2x + 5/2

Then I used the point slope form of a line to veryify.

y-y1 = m(x-x1)

y-0 = 1/2 (x-0)

y = 1/2x

A line parallel to this will have a slope 1/2.

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution:

* * The equation x - 2y = -5 can be solved for y to give us

y = 1/2 x + 5/2.

A line parallel to this will therefore have slope 1/2.

Then I used the point slope form of a line to veryify.

y - 0 = 1/2 * (x - 0) or

y = 1/2 x

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Self-critique (if necessary): OK

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Self-critique Rating: 3

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Question: * 2.3.68 / 28 (was 2.4.24) Perpendicular to x - 2 y = -5 containing (0,4) **** Give your equation for the

requested line and explain how you obtained it.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

First I solved the equation for y.

x - 2 y = -5

I subtracted x from both sides.

-2y = -x - 5

Then I divided both sides by -2.

This gave me:

y = 1/2x + 5/2

A line perpendicular to this will have a slope of -2/1 = -2.

Then I used the point slope form of a line to veryify.

y - 4 = -2 * (x - 0) or

y = -2 x + 4

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution:

* * The equation x - 2y = -5 can be solved for y to give us

y = 1/2 x + 5/2.

A line perpendicular to this will therefore have slope -2/1 = -2.

Point-slope form gives us

y - 4 = -2 * (x - 0) or

y = -2 x + 4. **

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Self-critique (if necessary): OK

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Self-critique Rating: 3

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Self-critique (if necessary):

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Self-critique rating:

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Self-critique (if necessary):

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Self-critique rating:

#*&!

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