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17. The equation [tex]y = 3x + 7[/tex] can be written in standard form as:

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To transform the given equation [tex]\(y = 3x + 7\)[/tex] into standard form, which has the structure [tex]\(Ax + By = C\)[/tex], follow these steps:

1. Start with the given equation:
[tex]\[ y = 3x + 7 \][/tex]

2. Rearrange the equation to move all the terms to one side. We want to have [tex]\(x\)[/tex] and [tex]\(y\)[/tex] on the left side of the equation and the constant term on the right side.

Subtract [tex]\(3x\)[/tex] from both sides to isolate the terms involving [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[ -3x + y = 7 \][/tex]

3. Multiply through by [tex]\(-1\)[/tex] (if necessary) to ensure that the coefficient of [tex]\(x\)[/tex] is positive, according to the standard form convention. In this case, the coefficient of [tex]\(x\)[/tex] is already positive when we rearrange, so this step isn't needed.

Therefore, the equation remains:
[tex]\[ 3x - y = -7 \][/tex]

In standard form [tex]\(Ax + By = C\)[/tex], the coefficients are:
[tex]\[ A = 3, \quad B = -1, \quad C = -7 \][/tex]

So, the equation [tex]\(y = 3x + 7\)[/tex] can be written in standard form as:
[tex]\[ 3x - y = -7 \][/tex]

Answer:

3x - y = - 7

Step-by-step explanation:

The equation of a line in standard form is

• Ax + By = C ( A is a positive integer and B, C are integers )

given the equation

y = 3x + 7 ( subtract 3x from both sides )

- 3x + y = 7 ( multiply through by - 1 )

3x - y = - 7 ← in standard form

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