course MTH 158 Mr. Smith,This is supposed to be assignment 19 according to our homework page. However, on the query, it is under assginment 18, which is why I titled this as section 2.4. I did not find an assignment for section 2.3. I sent you an email regarding this last night.
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20:45:14 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 --> since slope is 4/3 as the x int. increases by 3 units, the y int. increases by 4. from the point (-3,2) we have: -3+3 = 0 4+2 = 6 (0,6) 0 + 3 = 3 6 + 4 = 10 (3,10) 3+3=6 10 + 4 = 14 (6,14)
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20:45:53 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 --> right
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20:50:27 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 --> For points (2,2) (-1,1) first find the slope of the line using m=(y2 - y1)/(x2-x1) (1-2)/(-1-2) = -1/-3 = 1/3 y - y1 = m(x - x1) y + 1 = 1/3(x -2)
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20:52:24 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 used the points (2,2) as x1,y1 and (-1, 1 ) as x2,y2.
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20:56:24 **** 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 --> first find the slope with points (-4,0) and (0,4) m= (4-0)/(0+4) = 4/4 = 1 we know the y int. is 4 subsitute 4 for y in slope int. form equation to yield: y=x + 4
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20:56:39 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 --> right
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20:58:05 **** 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 --> from the slope int. form equation y=mx + b we know that 2 is m (the slope) and b is 1/2, the y intercept.
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20:58:28 ** 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 --> right
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