Assignment 18 23

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course Mth 158

3/6/13 Around 4:30PM

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:

 Graph the point (-3 , 2). Since the slope is 4 / 3, using Rise / Run, we move 3 units to the right of the point and then 4 units up to get (0 , 6) on the line same line. We repeat that step again to get (3 , 10). We can also reverse direction and, from point (-3 , 2), count three units to the left and 4 units down, receiving the point (-6 , -2).

 So, three other points on the same line:

 (-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:

 (2 - 1) / (2 + 1)

 Slope = 1/3

 y - 1 = 1/3(x + 1)

 y = 1/3x + 4/3

 

 

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): OK

 

 

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Self-critique Rating: OK

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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:

 Using the two intercepts given: (-4 , 0) and (0 , 4)

 (4 - 0) / (0 + 4)

 Slope = 4/4

 y - 0 = 1(x + 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): OK

 

 

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Self-critique Rating: OK

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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 = mx + b, m = slope of line, b = y-intercept

 y = 2x + 1/2

 Slope = 2, y-intercept = 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: OK

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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:

 x - 2y = -5

 y = 1/2x + 5/2

 Point-slope formula: (since it is parallel, it will have the same slope)

 y - 0 = 1/2(x - 0)

 y = 1/2x

 

 

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: OK

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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:

 x - 2 y = -5

 y = 1/2x + 5/2

 Point-slope formula: (using reciprocal of 1/2, since lines are perpendicular)

 y - 4 = -2(x - 0)

 y = -2x + 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: OK

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&#Very good work. Let me know if you have questions. &#