# Economics 101

**Topics:**Production-possibility frontier, Economics, Linear equation

**Pages:**11 (3106 words)

**Published:**September 11, 2013

Spring 2011

Answers to Homework #1

Due 2/2/11

Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework (legibly). Make sure you 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 will need that number when you submit exams and homework. Late homework will not be accepted 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 of the 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 + b and 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 point 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...

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