# Write Linear Equations In Standard Form Worksheet

## 6 problems

To write standard form for linear equations is $$Ax + By = C$$, where both $$A$$ and $$B$$ are non-zero integers and $$A$$, $$B$$, and $$C$$ are integers. $$A$$ is usually a positive integer. This form can be transformed to slope-intercept form for simpler graphing and behavior interpretation, and it is helpful for evaluating linear relationships.

Algebra 1
Linear Relationship

## How Will This Worksheet on "Write Linear Equations in Standard Form" Benefit Your Student's Learning?

• Rearranging equations is a practice that improves algebraic competence.
• Aids in understanding how lines and their attributes are represented in equations.
• Utilizes multiple step equation problems to foster critical thinking.
• Shows how to use linear equations in real-world situations.
• Establishes a solid basis for more complex mathematical ideas.
• Consistent practice helps build self-confidence in solving and interpreting equations.
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## Solved Example

Q. Determine the standard form of the following equation:$\newline$$y = 7x + 4$
Solution:
1. Rearrange equation for standard form: To rewrite the equation $y = 7x + 4$ in standard form, we need to rearrange the terms so that the $x$ and $y$ terms are on one side of the equation and the constant is on the other side. We want it in the form $Ax + By = C$.
2. Subtract $x$ term from both sides: The given equation is $y = 7x + 4$. To get it into standard form, we need to subtract $7x$ from both sides of the equation to move the $x$ term to the left side.
3. Adjust $x$ coefficient to be positive: Subtracting $7x$ from both sides gives us $-7x + y = 4$. This is almost in standard form, but we typically want the $x$ coefficient to be positive.
4. Multiply equation by $-1$: To make the $x$ coefficient positive, we can multiply the entire equation by $-1$. This gives us $7x - y = -4$.
5. Check coefficients for GCF: Now the equation is in standard form, $Ax + By = C$, with $A = 7$, $B = -1$, and $C = -4$. We need to check that $A$, $B$, and $C$ are integers whose greatest common factor (GCF) is $1$.
6. Verify standard form : The GCF of $7$, $-1$, and $-4$ is indeed $1$, so the equation is in standard form where A and B are not both zero, and A, B, and C are integers whose GCF is 1. .

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