ECO 108 Spring 2011 Math Appendix(1)

ECO 108 Spring 2011 Math Appendix(1) - ECO 108 Math and...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ECO 108 Math and Graph Appendix Spring 2011 A. Linear Functions A linear function is a function of the form f(x) = y = a + b*x (#) (# is simply a reference for this functional form.) where a and b are constants. The graph of a linear function is a straight line. The slope of a linear function is found by picking any two points on the line, say 1 1 2 2 ( x , y ) and ( x , y ), and determining the ratio of the vertical distance and horizontal distance between the points. slope = 2 1 2 1 y y vertical distance . horizontal distance x x - = - From the function, we can derive information about the line it generates: the slope, the vertical intercept and the horizontal intercept of the line. For the function (#), b = the slope a = the vertical intercept a b - = the horizontal intercept The vertical intercept is the value of y at which the line intersects the vertical axis. The horizontal intercept is the value of x at which the line intersects the horizontal axis. When the line intersects the horizontal axis, the value of the function is 0, i.e., the y-coordinate is zero. Thus, to solve for the horizontal intercept: y = a + b*x and y = 0 a + b*x = 0. So all have to do is solve a + b*x = 0 for x as a function of and b. b*x = – a x = a b - and as stated above, a b - is the horizontal intercept of the line. For example, consider y = 10 – (1/2)*x. If 1 1 2 2 ( x , y ) ( 8, 6 ) and ( x , y ) ( 12, 4), = = the slope of the line can be calculated as 2 1 2 1 y y 4 6 2 x x 12 8 4 - - - = = = - - – 1/2. Moreover, the vertical intercept is 10, and the horizontal intercept is 20. The following diagram shows a graph of this function as well as the points ( 8, 6 ) and ( 12, 4) and a rise – run illustration. Diagram A 0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 y x ( 8, 6 ) ( 12, 4 ) +4 - 2 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
B. Estimation vs. Computation of Slopes: Nonlinear Equation The function (#) from section A generates a straight line , i.e., b is a constant. Unlike linear functions, the graphs generated by nonlinear functions do not have constant slopes, i.e., the slope of a nonlinear curve is not the same at every point on the curve. Thus, the curve generated by a nonlinear function is not a straight line. The slope of any curve at a particular point on the curve is the slope of the straight line tangent to
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/05/2011 for the course ECO 108 taught by Professor Wolman during the Spring '08 term at SUNY Stony Brook.

Page1 / 6

ECO 108 Spring 2011 Math Appendix(1) - ECO 108 Math and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online