Assignments 8-9

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00:51:40 `q001. Note that this assignment has 4 questions For the function y = 1.1 x + .8, what are the coordinates of the x = 2 and x = 9 points? What is the rise between these points and what is the run between these points? What therefore is the slope between these points?

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RESPONSE --> The coordinates of the x=2 and x=9 points are (2,3) and (9, 10.7). The rise between the points is -7.7 and the run is -7, therefore the slope would be 11/10.

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00:54:10 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.

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RESPONSE --> i was almost fully correct. I got the negative signs mixed up and placed them where they shouldn't have, therefore it gave me -7.7 and -7, instead of both numbers positive. But I still got 1.1, but when 1.1 is put into a fraction, it is 11/10. Therefore I was right too.

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00:55:56 `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?

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RESPONSE --> In terms of a and b, the coordinates for the function are (a, 3) and (b, 10.7).

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00:58:39 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).

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RESPONSE --> I was almost correct. I used the y values for the last question instead of just plugging a and b into the equation and getting y = 1.1 a + .8 and y = 1.1 b + .8. I understand now. I thought the question meant to use the y values for the last question, which would have been (a, 3) and (b, 10.7).

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01:01:57 `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?

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RESPONSE --> The rise between the two points is 1.1a - 1.1b and the run is a - b. ???

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01:03:54 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.

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RESPONSE --> I was correct, except my rise was the opposite (1.1a - 1.1b) as that of my run (a-b). Does this matter?

As noted in your previous assignment, as long as you use the same order for the change in y as for the change in x, you're OK.

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01:07:24 `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.

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RESPONSE --> The average slope between the points is 1.1b - 1.1a / b - a, which after simpifying would leave the slope to be 1.1 - 1.1 = 0. ???

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01:09:37 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

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RESPONSE --> I didn't quite understand how to solve the question, but now i do. instead of canceling out the 1.1 to make 0 zero, the answer was actually 1.1, and i should have canceled out the b - a.

Right, but factor first, then cancel the common factor.

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01:17:41 `q001. Note that this assignment has 2 questions For the function y = 1.1 x + .8, what are the coordinates of the x = x1 point, in terms of the symbol x1? What are the coordinates of the x = x2 point, in terms of the symbol x2? What therefore is the rise between these two points, and what is the run? What is the average slope of the graph between these two points? Be sure to simplify your result.

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RESPONSE --> The coordinates for the two points are (x1, 1.1x1 + .8) and (x2, 1.1x2 + .8). The rise between the two points is 1.1x1 + .8 - 1.1x2 + .8 and the run is x1 - x2. The slope is 1.1(x1 - x2) / (x1 - x2) = 1.1.

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01:18:27 In terms of the symbol x1 the coordinates of the x = x1 point are ( x1, 1.1 x1 + .8) and the coordinates of the x = x2 point are ( x2, 1.1 x2 + .8). The rise between the two points is therefore rise = (1.1 x2 + .8) - (1.1 x1 + .8) = 1.1 x2 + .8 - 1.1 x1 - .8 = 1.1 x2 - 1.1 x1. The run is run = x2 - x1. The slope is therefore (1.1 x2 - 1.1 x1) / (x2 - x1) = 1.1 (x2 - x1) / (x2 - x1) = 1.1.

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RESPONSE --> I was correct.

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01:23:42 `q002. For the function y = 3.4 x + 7, what are the coordinates of the x = x1 point, in terms of the symbol x1? What are the coordinates of the x = x2 point, in terms of the symbol x2? What therefore is the rise between these two points, and what is the run? What is the average slope of the graph between these two points? Be sure to simplify your result.

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RESPONSE --> The coordinates for the points are (x1, 3.4x1 + 7) and (x2, 3.4x2 + 7). The rise between the two points is 3.4x2 + 7 - 3.4x1 + 7 and the run is x2 - x1. The average slope between these two points is 3.4(x2 - x1) / (x2 - x1) = 3.4.

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01:24:15 In terms of the symbol x1 the coordinates of the x = x1 point are ( x1, 3.4 x1 + 7) and the coordinates of the x = x2 point are ( x2, 3.4 x2 + 7). The rise between the two points is therefore rise = (3.4 x2 + 7) - (3.4 x1 + 7) = 3.4 x2 + 7 - 3.4 x1 - 7 = 3.4 x2 - 3.4 x1. The run is run = x2 - x1. The slope is therefore (3.4 x2 - 3.4 x1) / (x2 - x1) = 3.4 (x2 - x1) / (x2 - x1) = 3.4.

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RESPONSE --> I was correct.

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Good work. Let me know if you have questions.