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15 Cards in this Set
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Definition:
Linear equation in two variables 
Any equation that can be written in the form ax+by=c, a,b,c€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 a€R (no xintercept)


Vertical line

Can be written in the form x=a, where a€R (no yintercept)


Line throught the origin

can be written in the form ax+by=0 where a,b€R. (the x/yintercept is the same point, specifically the origin)


Slope

m=Δy/Δx=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,C€Z m=A/B


SlopeIntercept form

y=mx+b m=slope, yintercept (0,b)


PointSlope form

yy₁=m(xx₁) , (x₁,y₁) is a point on the line, m= slope
