Assignment 18

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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 --> ok

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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 --> ok

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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 --> ok

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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 --> ok

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Good work. Let me know if you have questions.