Math Final- Chapters 1-5 (Big Ideas)

Parallel and perpendicular

Parallel: line that passes (3,1) and is parallel to y=3x+1 Two ways to solve; point slope or slope int.

Point slope

(3,-1);m=-2 y+1=-2(x-3)

Slope intercept

(3,5) (4,6) Find slope and write in y=mx+b form

Compound inequalities

-3<2x+5<17

Arithmatic sequence

1,3,5,7,—,—,— List the next three numbers

Standard Form

Ax+By=C

Common difference

How much is +,-,x, or divided between values in arithmatic sequence. ex) 2,4,6,8 common difference: +2

Special systems

Infinite Solutions, No Solutions, and One Solution

Formula for Slope

m=y2-y1 ------ x2-x1

Fuction notation

f(x)=3x+1

Standard Form (graphing)

x+2y=6 To find each value plug in 0

Substitution

x=2y+6 y=3x-4 Plug the x value into the y value or The other way around

Point Slope form

y-y1=m(x-x1)

Elimination

y<3x+2 y<6x+7 Make one of the variables cancel out solve for x or y then plug the x or y value into one of the original problems

Graphing

y=4x-2 y=3x+4 Graph the two lines, where they cross is the solution

Slope Intercept form

y=mx+b

Slope intercept form graphing

y=mx+b m is the slope of the line b is the the y intercept

Inequalities

y>3x y<-2-x Plug in coordinates to solve Graph the inequalities to figure out where the two lines meet

Absolute Value

|x+2|<4 Remember to make two equations, one original the other opposite; |x+2|>-4