Answer :
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]
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
