Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
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
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
