Acc. College Algebra Sec.3.43.6Mangum
Terms
undefined, object
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Definition:
Linear equation in two variables  Any equation that can be written in the form ax+by=c, a,b,câ‚¬R and both a,b do not =0
 What is the relationship between the solutions to a linear equation in two variables and the graph on the equation?
 There are an infinite number of solutions, but not any pair will work. Only specific ones will.
 xintercept
 Where the line crosses the xaxis. The form of the poing will always be (x,0), where x is the crossing point.
 yintercept
 Where the line crosses the yaxis. The form of the point will always be (0,y) where y is the crossing point.
 Horizontal line
 Can be written in the form y=a, where aâ‚¬R (no xintercept)
 Vertical line
 Can be written in the form x=a, where aâ‚¬R (no yintercept)
 Line throught the origin
 can be written in the form ax+by=0 where a,bâ‚¬R. (the x/yintercept is the same point, specifically the origin)
 Slope
 m=Î”y/Î”x=y2y1/x2x1 where (x1,y1) and (x2,y2) are points on the line
 Four types of slope

positivem>0
negativem<0
zero slopem=0, horizontal line
undefined slope, vertical line  Parallel line
 The slopes of the two lines are the same
 Perpendicular lines
 The slopes of two lines are negative reciprocals of each other.
 Forms of linear equations (4)

Vertical line
Horizontal line
Standard form
SlopeIntercept form
PointSlope form  Standard form
 Ax+By=C, A>=0, A,B,Câ‚¬Z m=A/B
 SlopeIntercept form
 y=mx+b m=slope, yintercept (0,b)
 PointSlope form
 yyâ‚=m(xxâ‚) , (xâ‚,yâ‚) is a point on the line, m= slope