Assignment 18

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course Mth 158

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:

I found that with a slope of 4/3 and a point of (-3,2 ) by using rise over run that the points (-2,-6), (0,6) and (3,10) are all points on the same line.

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:

By using slope: m=(y2-y1) / (x2-x1)

M= (2-1)/ (2-(-1))

M=1/3 is the equation

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 little confused if I got the right answer or not.

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Self-critique Rating:

@&

From (-3, 2) to (-2,-6) the rise would be -8 and the run would be 1, so the slope would be -8 / 1 = 8.

So (-2, -6) would not be on this line.

A slope of 4/3 means that the rise / run ratio between any two points is 4/3.

One way of finding points on the line would be to start from a known point, and move 3 units on the horizontal direction and 4 units in the vertical direction.

*@

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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:

M= rise/run

= (4-0) / (0+4) = 1

y=mx+b = 1x+4

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 getx - y + 4 = 0.

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Self-critique (if necessary):

I think I got this right but I’m not sure

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Self-critique Rating:2

@&

You got this one. Good.

*@

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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:

Y= 2(0) +1/2 when Y intercept occures

Y= 1/2

Y intercept is (0,1/2)

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: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:

If it is parallel then the slope is ½ so:

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

and y = 1/2 x

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.

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):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.

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Your solution:

Since it is perpendicular y=1/2x+5/2

=-2/1 = 2

Point slope = y-4 = -2*(x-0)

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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