PS1_S - 1 METU Department of Economics Econ 101:...

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Unformatted text preview: 1 METU Department of Economics Econ 101: Introduction to Economics I Sections 01-02-03 2011-2012 Fall Semester Problem Set 1: Mathematics Review with SOLUTIONS PART A - QUESTIONS Q.1) Refer to the figure below. What is the expression of the slope of the line between points A and B? Slope of the line b/w points A and B: (The difference between Y2 and Y1 is the rise, or the change in Y. The difference between X2 and X1 is the run, or the change in X. The ratio of the changes is commonly called “rise over run.”) Q.2) Write the equations of the linear functions whose graph a. has slope 4 and intercept (0, 5) y = 5 + 4x b. has slope -3 and intercept (0, 0) y = – 3x c. has slope 3 and passes through the point (1, 1) y = -2 + 3x d. has slope -2 and passes through the point (2, -2) y = 2 – 2x e. passes through the points (2, 5) and (4, 7) y = x + 3 2 Q.3) Use the following figure to calculate the slope of the relationship: Q.4) Using the following figure; y b 70 a 50 30 c 20 Z Z 0 20 90 100 x a) What is the slope of the curve ZZ at point a? b) What is the slope of the curve ZZ at point b? c) What is the slope of the curve ZZ at point c? a) slope at point a is 3/2. b) slope at point b is 0. c) slope at point c is -3. Y a 2 b 6 8 10 6 1.5 X a) At points a and b. The slope at point a is -2 ( u Y / u X = – 4/2 = – 2) The slope at point b is -0.75. ( u Y / u X = -1.5/ 2 = – 0.75) b) Across the arc ab. The point a is (2, 6) and the point b is (6, 1.5). Vertical change between a and b is – 4.5 and horizontal change is 4. So, the slope across the arc ab is -1.125. 3 Q.5) Graph the following equations and indicate their respective slopes and intercepts. Explain whether the variables are positively or negatively related. a) 3y+45x=30 b) y-3x=6 c) 16y-4x+32=0 d) 6y+3x-18=0 a) y b) y 10 negatively related positively related slope= -15 slope=3 6 x x 2/3 -2 c) y positively related d ) y negatively related slope= ¼ slope= -1/2 3 8 x x 6 -2 Q.6) You are given two equations as follows: y = mx+b (1) z = - mx+b (2) where x, y, z are variables; b and m are positive constants . For the equations above; a) Define the dependent variables. b) Define the independent variables. c) Show the intercept and slope terms, and interpret them. 4 d) Explain whether the variables are positively or negatively related. Give economic examples of what the variables in equations may be....
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PS1_S - 1 METU Department of Economics Econ 101:...

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