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## MAT 211- Lecture 2- Section 15.1 (Cont.)

by: Brigette Maggio

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# MAT 211- Lecture 2- Section 15.1 (Cont.) MAT 211

Marketplace > Arizona State University > Math > MAT 211 > MAT 211 Lecture 2 Section 15 1 Cont
Brigette Maggio
ASU
GPA 3.9

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These notes cover MAT 211- Lecture 2 on Section 15.1 (Continued).
COURSE
PROF.
Dr. Mohacsy
TYPE
Class Notes
PAGES
6
WORDS
CONCEPTS
Math, MAT211
KARMA
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This 6 page Class Notes was uploaded by Brigette Maggio on Thursday January 14, 2016. The Class Notes belongs to MAT 211 at Arizona State University taught by Dr. Mohacsy in Fall 2015. Since its upload, it has received 17 views. For similar materials see Math for Business Analysis in Math at Arizona State University.

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Date Created: 01/14/16
MAT 211­ Lecture 2­ Section 15.1 (Continued) ­reviewed the table in the previous lecture’s class Linear Function General Formula with 2 Variables: z= f(x,y)= ax+by+c ­Ex.: z= ­1.1x+0.5y+xy NOT linear! because of the xy ­Ex.: z= ­1.1x +0.5y +10 NOT linear! because of the x  and y  (should be in first power) ­Ex.: z= ­x+5y+pi Linear! pi works! ­Ex.:  ­Each \$1 million increase in sales of x causes a \$2.7 million decline in sales of brand z.   a= ­2.7 ­Each \$1 million increase in sales brand y results in an increase of \$0.7 million in sales  of brand z. b= 0.7 ­All are selling \$6 million per pear. x=6, y=6, & z=6 6= ­2.7(6)+ 0.7(6)+c Find c! z= ­2.7x+ 0.7 y+c Graph of a Function: ­The graph of the function y= f(x) is the set of points with coordinate (x, y=f(x)) in the xy plane. ­Ex.: y=3x+2 x= 1.1 & y=5.3 The graph is a curve in the xy plane.  ­The Graph of a Function with 2 Variables: z= f(x,y) is the set of points with coordinates  (x,y, z=f(x,y)) is the x,y, z space. x=2, y=3, & z=1 *mutually perpendicular to each other* (2 units in the direction of x, 3 units in the direction of y, and 1 unit in the direction of z) ­There is an xy coordinate plane, a yz coordinate plane, and an xz coordinate plane. *­The graph of z= f(x,y) will be a surface (circle) in the x,y,z space. ­Ex.: 2­D y=0  (x­axis) & x=0 (y­axis) ­Ex.: 3­D z=0 (xy coordinate plane) (you don’t go up or down) ­Ex.: 3­D y=0 (xz coordinate plane) ­Ex.: 3­D x=0 (yz coordinate plane) ­Ex.: 2­D y=1 (horizontal line intersecting x­axis at y=1) ­Ex.: 2­D x=1 (vertical line intersecting y­axis at y=1) ­Ex.: 3­D z=1 (yes, linear!) (A plane that is parallel to the xy coordinate plane  shifted up 1 unit).             (xy plane +1) ­Ex.: 3­D x=3 (A plane that is parallel to the yz coordinate plane and intersects the  x­axis at x=3). ­Ex.: 3­D y=­1 (A plane parallel to the xz coordinate plane intersecting the y­axis at  y=­1). ­The graph of z= f(x,y) is a surface in the x,y,z space determined by the coordinates (x,y,&z). ­Ex.: 3­D Find the graph of (plane) z= f(x,y)= ­3x­2y+6. ­At which point the plane z= ­3x­2y+6 intersects the z­axis? x=0 & y=0 to find the z­intercept  z=6 ­At which point the plane z= ­3x­2y+6 intersects the x­axis? z=0 & y=0 0= ­3x+6 x=­2 ­y­intercept: 0=­2x+6y=3

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