Writing and Graphing Equations in Standard Form

Method

Writing a Linear Equation in Standard Form

Any linear equation can be rewritten in standard form. Consider the following linear equation that is written in slope-intercept form. y = 4/5x + 2/3 Using the Properties of Equality, the equation can be rewritten in standard form. Ax+By=C Here, A, B, and C are real numbers and A and B cannot both be equal to 0. It can be noted that representing A, B, and C with the smallest possible integers is preferred, as well as A being positive.

1
Remove All Fractions
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When a linear equation contains fractions, the first step is to remove all fractions. The equation is multiplied by the least common denominator of the fractions. In this case, it is the product of 5 and 3, which is 15. Using the Multiplication Property of Equality, the equation can be written as follows.

y= 4/5x + 2/3
15y=(4/5x+2/3)15
Simplify right-hand side
15y=4/5x* 15+2/3* 15
15y=4/5* 15* x+2/3* 15
15y=4* 15/5x+2* 15/3
15y=4* 3/1x+2* 15/3
15y=4* 3/1x+2* 5/1
15y=4* 3x+2* 5
15 y = 12x + 10

2
Rearrange the Terms of the Equation
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Now, move the terms containing variables to the left-hand side of the equation. In addition to this, move the constant to the right-hand side using the Subtraction Property of Equality.

15 y = 12x + 10
- 12x + 15y = 10

Since a positive coefficient for x is preferable, the equation can be multiplied by - 1.

- 12x + 15y = 10
12x-15y = - 10

This equation is now in the standard form. Note that the values of A, B, and C are in their smallest possible integer forms.

Exercises
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