Assignment 18

course Mth 158

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18:49:45

query 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 -->

Slope 4/3, point (-3,2)

x = -3 + 3 = 0

y = 2 + 4 = 6

(0,6)

x = 0 + 3 = 3

y = 6 + 4 = 10

(3,10)

x = 3 + 3 = 6

y = 10 + 4 = 14

(6,14)

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18:49:53

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 -->

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18:51:30

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)) = 1/3

y - 1 = 1/3(x + 1)

y = 1/3x + 4/3 or 3y - x = 4

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18:51:36

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 -->

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18:52:52

**** query 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 -->

(-4,0) (0,4)

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

y = 1x + 4 or 1x - y = -4

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18:53:00

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 -->

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18:54:21

**** query 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 -->

y = 2x + 1/2

slope = 2

y-intercept: 1/2

(0,1/2)

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18:54:33

** 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 -->

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Assignment 18

Good work. Let me know if you have questions.