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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.
x-intercept
Where the line crosses the x-axis. The form of the poing will always be (x,0), where x is the crossing point.
y-intercept
Where the line crosses the y-axis. 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 x-intercept)
Vertical line
Can be written in the form x=a, where a€R (no y-intercept)
Line throught the origin
can be written in the form ax+by=0 where a,b€R. (the x/y-intercept is the same point, specifically the origin)
Slope
m=Δy/Δx=y2-y1/x2-x1 where (x1,y1) and (x2,y2) are points on the line
Four types of slope
positive-m>0
negative-m<0
zero slope-m=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
Slope-Intercept form
Point-Slope form
Standard form
Ax+By=C, A>=0, A,B,C€Z m=-A/B
Slope-Intercept form
y=mx+b m=slope, y-intercept (0,b)
Point-Slope form
y-y₁=m(x-x₁) , (x₁,y₁) is a point on the line, m= slope