Economics 101Spring 2011Answers to Homework #1Due 2/2/11Directions: The homework will be collected in a box before the lecture. Please placeyour name, TA name and section number on top of the homework (legibly). Make sureyou write your name as it appears on your ID so that you can receive the correct grade.Please remember the section number for the section you are registered, because you willneed that number when you submit exams and homework. Late homework will not beaccepted so make plans ahead of time. Please show your work. Good luck!1. For each of the following sets of information write an equation. Assume that each set of information describes a linear relationship. Assume Y is the variable measured on the vertical axis and X is the variable measured on the horizontal axis. Write all equations in slope-intercept form. a. When X = 10, Y = 5 and when X = 7, Y = 2.Answer:First find the slope of the line: slope = rise/run = (5 – 2)/(10 – 7) = 1. Then, write the equation in general form: Y = mX + b and substitute one ofthe given points and the calculated slope into this general form to find the value of b. Thus, Y = X + b and using (X, Y) = (10, 5) we find b = -5. The equation is therefore Y = X – 5.b. When X = 12, Y = 6 and the slope of the line is equal to -5. Answer: Since you already are given the slope and a point on the line you can simply proceed to the general form: Y = mX + b and substitute the given point and the slope into this equation to find the value of b. Thus, Y = -5X + b and using (12, 6) we find b = 66. The equation is therefore Y = 66 - 5X.c. When X = 20, Y = 40 and the slope of the line is equal to 1.Answer:Since you already are given the slope and a point on the line you can simply proceed to the general form: Y = mX + b and substitute the given point and the slope into this equation to find the value of b. Thus, Y = X + band using (20, 40) we find b = 20. The equation is therefore Y = X + 20.d. (X, Y) = (4,4) and the slope of the line is equal to -20.Answer:Since you already are given the slope and a point on the line you can simply proceed to the general form: Y = mX + b and substitute the given 1point and the slope into this equation to find the value of b. Thus, Y = -20X+ b and using (4, 4) we find b = 84. The equation is therefore Y = 84 – 20X.e. (X, Y) = (14, -2) and the slope of the line is 2. Answer:Since you already are given the slope and a point on the line you can simply proceed to the general form: Y = mX + b and substitute the given point and the slope into this equation to find the value of b. Thus, Y = 2X + b and using (14, -2) we find b = -30 . The equation is therefore Y = 2X - 30.2. You are given the following information where each set of information describes two linear relationships. Use this information to determine what the (X, Y) values are that make both relationships simultaneously true. That is, use the information to solve for the answer (X, Y).a. The first line contains the points (3,5) and (8, 10) while the second line has a slope of -2 and contains the point (20, 10).Answer:Using the method provided in problem (1), you will want to find the equations for both lines and then use these two equations to solve for the solution (X, Y). The first equation is Y = X + 2 and the second equation is Y = 50 – 2X. The solution is therefore (X, Y) = (16, 18).b. The first line contains the point (20, 10) and has a slope of -1 while the second line has a y-intercept of 6 and a slope of 2. Answer:Using the method provided in problem (1), you will want to find the equations for both lines and then use these two equations to solve for the solution (X, Y). The first equation is Y = 30 - X and the second equation is Y = 2X + 6. The solution is therefore (X, Y) = (8, 22).c. The first line contains the point (10, 12) and has a slope of 5 while the second line has a x-intercept of 2 and a slope of 2. Answer:Using the method provided in problem (1), you will want to find the equations for both lines and then use these two equations to solve for the solution (X, Y). The first equation is Y = 5X – 38 and the second equation is Y = 2X - 4. The solution is therefore (X, Y) = (11.33, 18.66).2d. The first line contains the point (10, 900) and has a slope of -10 while the second line has a y-intercept of 20 and contains the point (20,100).Answer:Using the method provided in problem (1), you will want to find the equations for both lines and then use these two equations to solve for the solution (X, Y). The first equation is Y = 1000 – 10X and the second equation is Y = 4X + 20. The solution is therefore (X, Y) = (70, 300).3. You make a 70 out of a 100 possible points on your first midterm in your math class. On the second midterm you make an 80 out of a 100 possible points. If both exams are given equal weights in the calculation of your average, what must be true about your average score after the second midterm relative to your average score after the first midterm? Explain in words your answer. In your answer discuss what your average score is after the first midterm and what your average score is after the second midterm.Answer:Your average score in the class must have increased after the second midterm: your average score in the class after the first midterm is equal to70, while your average score in the class after the second midterm is equal to (70 + 80)/2 = 75. When the additional midterm score is higher than your previous average score, then your overall average must increase. This concept is one that we will use repeatedly later in the course. 4. You make a 40 out of a possible 50 points on your first midterm in psychology. a. On a 100 point scale what is your grade?Answer:To convert this score to a 100 point scale use the following equation which equates two ratios: 40/50 = X/100. Solving for X, we find that this score of 40 on a 50 point test is equivalent to a score of 80 on a 100 point test. b. Suppose the second midterm is graded on a 40 point scale. In order for your average in the class …
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