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.