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The problem asks to find the equation of a line that is:

1. **Parallel** to the line given by \( y = 3 - 9x \), and
2. Passes through the **origin** (point \( (0,0) \)).

### Step-by-Step Solution:

1. **Identify the slope of the given line**:
   - The equation \( y = 3 - 9x \) is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   - Comparing \( y = 3 - 9x \) with \( y = mx + b \), we can see that the slope \( m = -9 \).

2. **Use the same slope**:
   - Since the line we need to find is **parallel** to the given line, it must have the same slope. So, the slope of the required line is also \( -9 \).

3. **Equation of the line through the origin**:
   - The general form of a line equation with slope \( m \) passing through the origin is \( y = mx \).
   - Since the slope is \( -9 \), the equation becomes:
     \[
     y = -9x
     \]

Thus, the equation of the line that is parallel to \( y = 3 - 9x \) and passes through the origin is:

\[
\boxed{y = -9x}
\]

Would you like further clarification or details on any steps?

### Related Questions:
1. How do you find the slope of a line from its equation?
2. What does it mean for two lines to be parallel?
3. How do you convert a line equation into slope-intercept form?
4. How do you determine if a point lies on a line?
5. How would the equation change if the line passed through a different point?

**Tip:** For lines passing through the origin, the y-intercept is always zero, making the equation simpler.

Find the equation of the line that is parallel to y = 3 - 9x and that passes through the origin.

Learn how to find the equation of a line that is parallel to y = 3 - 9x and passes through the origin. This problem involves using the slope-intercept form and properties of parallel lines. Suitable for students in Grades 8-10.

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