Linear Systems

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Geo

luonut Fernando De Francesca

Rate of Change

luonut Lina Fahimah Ali

Math Summative

luonut Mainal Lodhra

1.1 Understand computer storage and data types

luonut Gary Sibbitts

Linear Systems

Slope(m)

Finding Slope

Slope Formula

y2-y1 _____ x2-x1

Slope= Undefined when line is vertical

Slope = 0 when line is horizontal

Linear Equations

Standard Form

Standard Form to Slope Intercept Form

Isolate y

Move everything to the right side of the = sign except y

Numbers sign changes when moved over = sign

2x+y=8

y=-2x+8

Ax+By=C

A,B,C = Constants (Only Whole Numbers)

Slope Intercept Form

x,y=variables

x = independent variable

y = dependent variable

b=y intercept

m=slope

What is a Linear System

Constant rate of change

Lines are always straight

System made of 2 or more lines

Solving Linear Systems

Elimination

Convert both equations to Standard Form

Ax+By=C

Choose a variable to eliminate

Multiply both equations by a number to make the coefficients same or opposite

Add/Subtract the equations to eliminate the chosen variable

Sub in value of variable that you solved to find the other variable

Graphing

Make both equations Slope Intercept Form

y=mx+b

Start each line at y-int(b)

Use the equation of the slope to draw the lines

If slope is positive, line increases from left-right

If slope is negative, line decreases from left-right

Substitution

Solve for a variable by rearranging to make everything = a variable

Sub in value of variable that you solved to find the other variable