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# Chapter 3

### Linear functions

Constant increase situation y=2x+5; 5 is the y-intercept or INITAL CONDITION or staring point in the situation; graph slants up from left to right; positive slope
LINEAR FUNCTION (SLOPE INTERCEPT FORM) y=mx=b or f(x)=mx+b
Constand decrease situation y=-2/3x=50; graph slants down from left to right; negative slope
PIECEWISE LINEAR union of segments or pieces of two or more linear functions
LINEAR COMBINATION EX: 20P + 32L
STANDARD FORM OF AN EQUATION FOR A LINE Ax+By=C; graph where A and B are not both 0 is a line
Horizontal line slope=0; y= #
Vertical line slope undefined; x=#
Oblique line Ax+By=C; A and B both not 0; slope= -A/B
POINT-SLOPE THEOREM If al ine contains (x1,y1) and has slope m, then it has equation y-y1=m(x-x1)
Find an eqaution of the line thorugh (3,5) (6, -1) 1) find slope; m=-2 2)use ponit-slope form with either point; y-5=-2(x-3) 3) standard form; 2x+y=11
ARITHMETIC SEQUENCE a sequence with a constant difference between successive terms
RECURSIVE FORMULA a1 an=an-1+d
EXPLICIT FORMULA an= a1+(n-1)d
GREATEST INTEGER SYMBOL [] (round down) EX: [2 3/4]=2; [-2.1]=-3
EX: Bottles are oackaged in cartons of 8. Write an equation that gives the nmber of complete cartons c packaged each day, if the company prepares b bottles each day. c=[b/8]
Created by: jessries0139