course Mth 158
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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Self-critique (if necessary):
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Self-critique Rating:
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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:
Given the slope 4/3 with a run of 3 and a rise of 4, the point (-3, 2) will have (0, 6) (3, 10) points on the line as well.
Starting with (-3, 2) you would move 3 units to the right on the x axis, and 4 units on the y axis to give you the point (0, 6) From there you would move 3 units right on the x axis and 4 units on the y axis giving you the point (3, 10)
..this would continue on adding 3 units to the x axis point and adding 4 units to the y axis point.
You could also move in the other direction with negative points by adding slope -4/-3 to get the first point (-6, -2)
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:
My answer was a little different, but with the same concept. I believe any answer to this question could vary slightly.
You chose different x intervals, which is perfectly valid. Your solution is very good.
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 dont know where the question went on this one?? But from the book, it appears to be Q 2.3.40 which states Find the equation of the line L which has points (-1, 1), (2, 2)
First you find the slope by using the formula for slope y y1 = m(x x1)
2 1 / 2 - (-1) = 1/3 Gives us a slope with a run of 3 and a rise of 1
The point slope formula is
y - y1 = m (x-x1) substituting we have
y 1 = 1/3 (x (-1)) distribute and solve
y 1 = 1/3x + 1/3
y = 1/3x + 1/3 + 1
y = 1/3x + 4/3
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Self-critique Rating: 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:
The given points are (-4, 0) and (0, 4)
First you would find the slope
4-0 / 0-(-4) = 1
Then use the equation of a line in slope-intercept form
y = mx + b
If x intercept is -4 and y intercept is 4 then
y = 1x + 4
-x + y = 4 or 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.
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Self-critique (if necessary):
Im not sure if my solution is correct. I followed the example in the book which leaves 2 solutions (example problem 2.3.51) Did I do it correctly?
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.
Still another 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 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:
In y = 2x + ½ it is written in slope intercept form so we compare it to
y = mx + b where the slope is 2 and the y intercept is 1/2
confidence rating: 1
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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):
I followed the book to get my solution, but I did not understand it to be written: the y intercept is (0, ½) although I can see why it would be.
Would the slope always be the number(x) if it is written in slope intercept form??
The slope-intercept form is
y = m x + b,
where m is the slope and b is the y-intercept.
We do say that b is the y-intercept.
The graph actually intercepts the y axis at the point (0, b), so we can also say that the y-intercept is the point (0, b).
So in this example, it is correct to say that the y-intercept is 1/2, and it is also correct so that that the y-intercept is the point (0, 1/2). The two statement mean exactly the same thing.
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Self-critique Rating: 3
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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.
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Your solution:
Parallel to the line x 2y = -5; containing the point (0, 0)
It would be a horizontal line
To find x substitute 0 for y
x 2(0) = -5
x = -5 first point(-5, 0)
To find y substitute 0 for x
0 2y = -5
-2y = -5 divide both sides by -2
y = 5/2 Second point (0, 5/2)
Which lies in a straight line on the x axis.
Slope is 5/2 0 / 0 (-5) = ½
It appears that you found two points on the line x - 2 y = -5, then used these two points to get the slope.
That is excellent reasoning, and you did it accurately. So you did very good work to arrive at this correct conclusion.
However note that is would have been much easier to put the equation in slope-intercept form:
x - 2y = -5 so
y = 1/2 x - 5,
from which you can immediately conclude that the slope is 1/2.
Either way, your entire solution is valid.
with a run of 2 and a rise of 1
y y1 = m(x x1)
y 0 = ½ ( x 0)
y = 1/2x 1/2x y = 0 or y = 1/2x
I really have no idea if I did that right
.I will have to check the given solution
confidence rating: 1
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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.
Point-slope form gives us
y - 0 = 1/2 * (x - 0) or just
y = 1/2 x. **
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Self-critique (if necessary):
It appears to be right. I have the right outcome, but I am not sure if I found it the right way.
You got a very good solution. However be sure to see my note for an easier way to find the slope of the original line.
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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.
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Your solution:
Perpendicular to the line x 2y = -5; containing the point (0, 4)
To find x replace y by 0
x 2(0) = -5
x = -5 First point (0, -5)
find y replace x by 0
0 2y = -5
-2y = -5 divide both sides by -2
y = 5/2 Second point (4, 5/2)
Slope = 5/2 (-5) / 4 0 = 15/2 / 4 = 15/8
Run = 8 Rise = 15
y y1 = m(x x1)
y (-5) = 15/8 ( x 0)
y + 5 = 15/8x
I dont think this is the right way??
You made a simple arithmetic error.
Your procedure was valid, but it's easier to put the equation into slope-intercept form, with fewer steps and less chance of an arithmetic error.
See my note below.
Maybe I can just use this formula with the given information? x - 2 y = -5 containing (0,4)
y y1 = m(x x1)
y 4 = Now I am confused? I dont know the slope of this line. See, I dont know how it is that I can solve one problem and then the very next one throws me for a loop. What am I doing wrong here?
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. **
How did you get y = 1/2x + 5/2 ??
x - 2y = -5 so by subtracting x from both sides we get
-2y = -x - 5. Multiplying both sides by -1/2 we get
y = -1/2 ( -x - 5). By the distributive law we have
y = -1/2 * (-x) - 1/2 * (-5). Simplifying this is
y = 1/2 x + 5/2.
You are doing some very good work here. Sometimes you take the 'long way around', using reasoning that is valid but requires more steps so is more error-prone. Sometimes, to your great credit, you get through all those steps without making any errors.
See my notes and let me know if you have additional questions.