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Here are some tips for Linear Equations, which aligns with Hawaii state standards:
Linear Equations
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
Note: For Method B, with negative slopes, the change is the opposite.
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 = -1When x = 1, y = -1
so when x = 2, y = -1 + 2 = 1When x = 0, y = -3
so when x = -1, y = -3 - 2 = -5When x = -1, y = -5
so when x = -2, y = -5 - 2 = -7
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.
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