Acc. College Algebra- Sec.3.4-3.6-Mangum

Front 1

Definition:
Linear equation in two variables

Back 1

Any equation that can be written in the form ax+by=c, a,b,c€R and both a,b do not =0

Front 2

What is the relationship between the solutions to a linear equation in two variables and the graph on the equation?

Back 2

There are an infinite number of solutions, but not any pair will work. Only specific ones will.

Front 3

x-intercept

Back 3

Where the line crosses the x-axis. The form of the poing will always be (x,0), where x is the crossing point.

Front 4

y-intercept

Back 4

Where the line crosses the y-axis. The form of the point will always be (0,y) where y is the crossing point.

Front 5

Horizontal line

Back 5

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

Front 6

Vertical line

Back 6

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

Front 7

Line throught the origin

Back 7

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

Front 8

Slope

Back 8

m=Δy/Δx=y2-y1/x2-x1 where (x1,y1) and (x2,y2) are points on the line

Front 9

Four types of slope

Back 9

positive-m>0
negative-m<0
zero slope-m=0, horizontal line
undefined slope, vertical line

Front 10

Parallel line

Back 10

The slopes of the two lines are the same

Front 11

Perpendicular lines

Back 11

The slopes of two lines are negative reciprocals of each other.

Front 12

Forms of linear equations (4)

Back 12

Vertical line
Horizontal line
Standard form
Slope-Intercept form
Point-Slope form

Front 13

Standard form

Back 13

Ax+By=C, A>=0, A,B,C€Z m=-A/B

Front 14

Slope-Intercept form

Back 14

y=mx+b m=slope, y-intercept (0,b)

Front 15

Point-Slope form

Back 15

y-y₁=m(x-x₁) , (x₁,y₁) is a point on the line, m= slope