Write equations in standard form

key notes:

What is Standard Form?

A linear equation in Standard Form is written as:

Ax+By=C

where:

• A, B and C are integers
• A should be non-negative (A ≥ 0)
• x and y are variables
• No fractions or decimals are allowed

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Why Use Standard Form?

• Useful for finding intercepts quickly
• Common in word problems and real-life situations
• Makes comparing equations easier

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Converting from Slope-Intercept Form to Standard Form

Slope-Intercept Form:

y=mx+b

Steps:

1. Move the x-term to the left side (so both x and y are on the same side).
2. Remove fractions or decimals by multiplying through by the denominator.
3. Make sure A≥0 and all coefficients are integers.

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Example 1
Convert y=2x+3 to standard form:
Step 1: Move 2x to left:

−2x+y=3

Step 2: Multiply by -1 (to make A>0):

2x−y=−3

✅ Standard Form:

2x−y=−3

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Example 2
Convert y=3/4x−2 to standard form:
Step 1: Move 3/4x to left:

−3/4x+y=−2

Step 2: Multiply all terms by 4 to clear fraction:

−3x+4y=−8

Step 3: Multiply by -1:

3x−4y=8

✅ Standard Form: 3x−4y=8

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From Point-Slope Form to Standard Form

Point-Slope Form:

y−y₁=m(x−x₁)

Expand, simplify, and arrange into Ax+By=C

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Key Rules for Standard Form

• A, B, C are integers (no fractions/decimals)
• A≥ 0
• Write x first, then y, then constant

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Practice Problems

Convert to standard form:

1. y=−3x+7
2. y=2/5x+4
3. y−3=5(x−2)
4. y=0.5x−6

Learn with an example

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