Assignment 18

course Mth 158

???????????assignment #018018. `query 18

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College Algebra

07-03-2007

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12:15:40

2.4.30 (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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RESPONSE -->

I found points (1, 5) (5, 8) and ( 9, 11) by adding 4 to each x-axis point and adding 3 to each point on the y-axis.

confidence assessment: 1

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12:18:07

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).

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RESPONSE -->

I see what I did wrong I moved in the wrong direction. I understand how to get the corect answers.

self critique assessment: 2

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12:33:48

query 2.4.36 (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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RESPONSE -->

First I found the slope m = (2 - 1) / ( 2 - (-1) ) = 1/ 3. Using y - y1 = m(x - x1)

y - 2 = 1/3x - 2

y = 1/3x + 0

confidence assessment: 1

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12:35:44

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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RESPONSE -->

I got the slope right, but I'm not sure how to find the y-intercept. I see how you solved for y but I don;t understand how the y-intercept is 4/ 3.

self critique assessment: 2

In the form y = m x + b, m is the slope and b is the y intercept.

y = 1/3 x + 4/3 is of the form y = m x + b with m = 1/3 and b = 4/3.

You can also see this by sketching the line segment between the given points (-1, 1) and (2, 2). The rise between these points is 1, the run is 3 so the slope is 1/3. If you move 1 unit in the x direction from (-1, 1) you will therefore move 1/3 of a unit in the y direction, ending up at the point (0, 1 + 1/3) = (0, 4/3).

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12:40:10

2.4.46 (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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RESPONSE -->

I found the slope using the points ( -4, 0) and ( 0, 4)

m= ( 4 - 0 ) / ( 0 - (-4) ) = 4/4 = 1. Since the y-int is already given the equation for this line is y = 1x + 4

confidence assessment: 2

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12:40:56

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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RESPONSE -->

Thats is how I did it. I know that you don't need the 1 in front of the x , but it helps me to remember what is supposed to be there.

self critique assessment: 2

That's fine. I sometimes put it there for emphasis.

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12:42:05

2.4.56 (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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RESPONSE -->

The slope is 2 and the y-int is 1/2. I know this because of the slope-intercept form of an equation of a line where y = mx + b. M is the slope and b is the y-int.

confidence assessment: 3

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12:42:46

** 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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RESPONSE -->

I just forgot to express the y-int as a point I know that the x-corrodinate of the y-int is always 0.

self critique assessment: 2

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