https://file.aiquickdraw.com/mathbot/file/17276937548925emcuczx.jpg

give me the standard linear form and identity A,B,C.

To convert the equations from your image into their standard form and identify the coefficients \(A\), \(B\), and \(C\), let's analyze each equation.

### General Standard Form for Linear Equations:
The general form of a linear equation in two variables is:
\[
Ax + By = C
\]
Where:
- \(A\), \(B\), and \(C\) are constants.
- \(x\) and \(y\) are variables.

### Equation 1:
The given equation is:
\[
1.5y = 9x - 9
\]
Rearrange this to fit the standard form:
\[
-9x + 1.5y = -9
\]
Multiply the entire equation by 2 to remove the decimal:
\[
-18x + 3y = -18
\]
Now, the equation is in standard form. So:
- \(A = -18\)
- \(B = 3\)
- \(C = -18\)

### Equation 2:
The given equation is:
\[
2 \cdot \frac{1}{2}y + 5 = 6y
\]
Simplify the left side:
\[
y + 5 = 6y
\]
Rearrange to bring terms involving \(y\) on one side:
\[
y - 6y = -5
\]
\[
-5y = -5
\]
So, divide by \(-5\):
\[
y = 1
\]
This equation is not linear in terms of both \(x\) and \(y\), but rather expresses \(y\) as a constant.

### Equation 3:
The given equation is:
\[
2x + 4 = 6y
\]
Rearrange to fit the standard form:
\[
2x - 6y = -4
\]
Thus, in standard form:
- \(A = 2\)
- \(B = -6\)
- \(C = -4\)

### Equation 4:
The given equation is:
\[
2x = 4y - 8
\]
Rearrange to fit the standard form:
\[
2x - 4y = -8
\]
Thus, in standard form:
- \(A = 2\)
- \(B = -4\)
- \(C = -8\)

### Equation 5:
The given equation is:
\[
3y - 6 = 4x
\]
Rearrange to fit the standard form:
\[
4x - 3y = -6
\]
Thus, in standard form:
- \(A = 4\)
- \(B = -3\)
- \(C = -6\)

---

### Summary of Coefficients \(A\), \(B\), and \(C\):

1. **Equation 1**: \(A = -18\), \(B = 3\), \(C = -18\)
2. **Equation 2**: \(y = 1\) (Not in the general linear form)
3. **Equation 3**: \(A = 2\), \(B = -6\), \(C = -4\)
4. **Equation 4**: \(A = 2\), \(B = -4\), \(C = -8\)
5. **Equation 5**: \(A = 4\), \(B = -3\), \(C = -6\)

Would you like to ask more about any of these solutions or require additional explanations?

### Related Questions:
1. How can you solve a system of linear equations with these forms?
2. What are the key properties of linear equations in two variables?
3. How can graphing help in visualizing solutions of these equations?
4. What is the difference between consistent, inconsistent, and dependent systems?
5. How do changes in coefficients \(A\), \(B\), or \(C\) affect the line's slope and intercepts?

### Tip:
When rearranging equations to the standard form, always ensure the coefficient of \(x\) is on the left, and watch for sign changes when moving terms across the equal sign.

Write the following in a standard form and identify A, B, C.

Learn how to convert linear equations into standard form (Ax + By = C) and identify the coefficients A, B, and C. This detailed solution includes step-by-step instructions for solving equations and removing decimals. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation