Assignment 18

course MTH 158

For Section 2.4

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019. `query 19

College Algebra

10-25-2007

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assignment #018

018. `query 18

College Algebra

10-25-2007

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14:02:19

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 -->

x runs 3 and y rises 4,

(1,6) (4,10) (7,14)

confidence assessment: 3

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14:05:05

10-25-2007 14:05:05

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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NOTES ------->

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14:07:32

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 -->

m=(2-1)/[2-(-1)] m=1/3

y=mx+b

y=(1/3)x+1

I first found the slope of the points, then used the slope intercept formula to find the equation.

confidence assessment: 3

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14:08:27

10-25-2007 14:08:27

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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NOTES -------> I used the wrong formula.....

note that you can check your results on questions of this nature by verifying that the points are actually on the graph. If x = -1 you should get y = 1, to verify (-1, 1); and if x = 2 you should get y = 2 to verify the point (2, 2).

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14:11:59

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 -->

x intercept points (-4,0) y intercept points are (0,4)

first determine the slope:

m=(4-1)/[0-(-4)]

m=3/4

m=(4-0)/[0-(-4)] = 1; looks like you made a simple typo. Otherwise the solution looks good.

slope is 3/4

y-y1=m(x-x1)

y-0=3/4[x-(-4)]

y=3/4x+3

confidence assessment: 3

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14:12:13

10-25-2007 14:12:13

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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NOTES ------->

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14:13:24

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 -->

using the standard formula y=mx+b

m=slope

slope is 2

the y intercept is b=1/2

confidence assessment: 2

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14:13:52

** 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 -->

the y intercept is (0, 1/2) not 1/2.

self critique assessment: 3

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