#$&* course Mth 163 11:19 pm 10/4/2014 008.
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Given Solution: Evaluating y = 1.1 x +.8 for x = 2 and x = 9 we obtain y = 3 and y = 10.7. The graph points are therefore (2,3) and (9,10.7). The rise between these points is 10.7 - 3 = 7.7 and the run is 9-2 = 7. Thus the slope is 7.7 / 7 = 1.1. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating: OK ********************************************* Question: `q002. For the function y = 1.1 x + .8, what are the coordinates of the x = a point, in terms of the symbol a? What are the coordinates of the x = b point, in terms of the symbol b? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: In this function a would equal 1.1 and b would equal .8 A = 1.1 B = .8 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 2
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Given Solution: If x = a, then y = 1.1 x + .8 gives us y = 1.1 a + .8. If x = b, then y = 1.1 x + .8 gives us y = 1.1 b + .8. Thus the coordinates of the x = a point are (a, 1.1 a + .8) and (b, 1.1 b + .8). &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I did not answer this problem appropriately. I did not understand what the question was asking for, looking back I see that it requested coordinates and I had overlooked that previously. ------------------------------------------------ Self-critique rating: 3 ********************************************* Question: `q003. We see that the coordinates of the x = a point are (a, 1.1 a + .8) and (b, 1.1 b + .8). What therefore is the rise between these two points? What is the run between these two points? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The rise between these 2 points would be (1.1 b + .8) - (1.1 a + .8). The run between these 2 points would be b - a. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
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Given Solution: The rise between the points is the rise from y = 1.1 a + .8 to y = 1.1 b + .8, a rise of rise = (1.1 b + .8) -(1.1 a + .8) = 1.1 b + .8 - 1.1 a - .8 = 1.1 b - 1.1 a. The run is from x = a to x = b, a run of run = b - a. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I failed to simplify the equation for the rise which would have been fairly simple after applying the distribution method. This makes one of the .8 a negative which cancels the other out since it is positive. ------------------------------------------------ Self-critique rating: 3 ********************************************* Question: `q004. We see that the rise between the x = a and x = b points of the graph of y = 1.1x +.8 is 1.1 b + .8 - (1.1 a + .8), while the run is b - a. What therefore is the average slope of the graph between these points? Simplify your answer. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The average slope between these points is found with the equation: (1.1 b - 1.1 a)/ b - a Simplifying (1.1 b - 1.1 a) results in 1.1(b -a)/ b- a then this simplifies to 1.1 after division occurs. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
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Given Solution: The slope is slope = rise / run = (1.1 b - 1.1 a) / (b - a) = 1.1 (b - a) / (b - a) = 1.1. The significance of this series of exercises is that the slope between any two points of the straight line y = 1.1 x + .8 must be 1.1, no matter whether the points are given by numbers (e.g., x = 2 and x = 9) or by symbols (x = a and x = b). Mostly &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK The fact is that m = slope in then equation y = mx + b ------------------------------------------------ Self-critique rating: OK If you understand the assignment and were able to solve the previously given problems from your worksheets, you should be able to complete most of the following problems quickly and easily. If you experience difficulty with some of these problems, you will be given notes and we will work to resolve difficulties. ********************************************* Question: `q005. What are the rise, run and slope of the graph of the function y = 3/2 x + 12 between x = 2 and x = 4? In terms of the symbols a and b, what are the rise, run and slope of the graph of the same function between x = a and x = b? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: y = 3/2 * 2 + 12 6/2 +12 3+12 Y = 15 y = 3/2 * 4+ 12 12/2 + 12 6+ 12 Y = 18 Making the points: (2, 15) and (4, 18) The rise would be 18-15 = 3 The run would be 4-2 = 2 And the slope would be rise/run which is 3/2 which is also m. For X =a and x =b y = 3/2 a + 12 y = 3/2 b + 12 Which makes the rise: (3/2 b + 12) -(3/2a +12) and the run b - a (3/2 b - 3/2 a) / b - a 3/2 (b -a ) / b - a Which makes the slope 3/2 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3 ------------------------------------------------ Self-critique rating: OK "" " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: OK "" " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!