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

  

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.

 

Your solution:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

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.

 

Your solution:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

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.

 

 

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique Rating:

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?

 

Your solution:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

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).

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.

 

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique Rating:

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?

 

Your solution:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

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.**

 

 

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique Rating:

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.

 

 

 

Your solution:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

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.

 

Point-slope form gives us

 

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

y = 1/2 x. **

 

 

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique Rating:

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.

 

Your solution:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

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. **

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique Rating: