4. Express the equation x = 3y in the form of ax + by + c = 0 and find the values of a, b and c.

To express the equation \( x = 3y \) in the form \( ax + by + c = 0 \), follow these steps:

### Step 1: Rearrange the equation to match the required form

Given equation: 
\[
x = 3y
\]

Subtract \( 3y \) from both sides to move all terms to one side of the equation:

\[
x - 3y = 0
\]

### Step 2: Identify the coefficients \( a \), \( b \), and \( c \)

Now, compare this equation with the standard form \( ax + by + c = 0 \):

\[
x - 3y + 0 = 0
\]

Here, the coefficients are:

- \( a = 1 \) (coefficient of \( x \))
- \( b = -3 \) (coefficient of \( y \))
- \( c = 0 \) (constant term)

### Final Answer:

The equation \( x = 3y \) expressed in the form \( ax + by + c = 0 \) is:

\[
1x - 3y + 0 = 0
\]

So, the values are:

\[
a = 1, \quad b = -3, \quad c = 0
\]

Would you like any further details or have any questions?

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Here are 5 related questions for practice:

1. Express the equation \( 2x + 5 = y \) in the form \( ax + by + c = 0 \) and find the values of \( a \), \( b \), and \( c \).
2. Convert the equation \( y = 4x - 7 \) into the form \( ax + by + c = 0 \) and identify \( a \), \( b \), and \( c \).
3. Write \( 3x + 2y = 6 \) in the form \( ax + by + c = 0 \) and state the values of \( a \), \( b \), and \( c \).
4. Express \( 5y - 10x = 15 \) in the form \( ax + by + c = 0 \) and determine \( a \), \( b \), and \( c \).
5. Rearrange \( y = -2x + 8 \) into the form \( ax + by + c = 0 \) and find \( a \), \( b \), and \( c \).

**Tip:** When converting an equation to the form \( ax + by + c = 0 \), make sure all terms are on one side, leaving zero on the other.

Learn how to express the equation x = 3y in the form ax + by + c = 0 with detailed steps and examples. This problem involves rearranging equations and identifying coefficients, covering key algebraic concepts. Suitable for students in Grades 7-9.

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