Linear Equations Sample Problems

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Here are some tips for Linear Equations, which aligns with California state standards:

Linear Equations

This topic will be easier if you know how to simplify expressions and do variable substitutions.
To review the Simplifying Algebraic Expressions topic, see here.
To review the Variable Substitution topic, see here.

Step 1: Simplify the given equation to the form of y = mx + b

^-3x + ^-6 + 3y = 4y - 5x - 3 Given equation

^-3x + ^-6 + 3y - 4y = - 5x - 3 Move y terms to the left side

3y - 4y = - 5x - 3 + 3x + 6 Move x terms and constants to the right side

^-y = ^-2x + 3 Combine like terms

y = 2x - 3 Multiply by ^-1 to have a positive y

Step 2: Substitute x = 0

y = 2x - 3

= 2(0) - 3

= 0 - 3

= ^-3

Step 3: Fill in the other values

Method A: Substitute x values Method B: Use the slope (m)

x = ^-2: y = 2(^-2) - 3 = ^-7

x = ^-1: y = 2(^-1) - 3 = ^-5

x = 1: y = 2(1) - 3 = ^-1

x = 2: y = 2(2) - 3 = 1

The slope is 2.
As x changes by +1, y changes by +2.
As x changes by -1, y changes by -2.
When x = 0, y = ^-3
so when x = 1, y = ^-3 + 2 = ^-1
When x = 1, y = ^-1
so when x = 2, y = ^-1 + 2 = 1
When x = 0, y = ^-3
so when x = ^-1, y = ^-3 - 2 = ^-5
When x = ^-1, y = ^-5
so when x = ^-2, y = ^-5 - 2 = ^-7

Note: For Method B, with negative slopes, the change is the opposite.
Take slope m = ^-5 as an example.
When x changes by +1, y changes by -5.
When x changes by -1, y changes by +5.

^-3x + ^-6 + 3y	=	4y - 5x - 3	Given equation
^-3x + ^-6 + 3y - 4y	=	- 5x - 3	Move y terms to the left side
3y - 4y	=	- 5x - 3 + 3x + 6	Move x terms and constants to the right side
^-y	=	^-2x + 3	Combine like terms
y	=	2x - 3	Multiply by ^-1 to have a positive y