make a parallel to y=-2/1+1 that goes through the Origen 0,0

To find the equation of a line parallel to the line \( y = -\frac{2}{1} + 1 \) that passes through the origin \((0,0)\), let's follow these steps:

### 1. Simplify the Given Equation:
The given equation can be rewritten as:
\[
y = -2 + 1
\]
which simplifies to:
\[
y = -1
\]

However, this looks like a misunderstanding in interpreting the equation. If we assume the equation was intended to be:
\[
y = -2x + 1
\]
then we proceed with this version.

### 2. Identify the Slope:
The slope of the given line \( y = -2x + 1 \) is \(-2\).

### 3. Use the Point-Slope Form:
For a line parallel to the given one, the slope will be the same (\(-2\)). Since it must pass through the origin \((0,0)\), the equation can be written in point-slope form:
\[
y - y_1 = m(x - x_1)
\]
where \(m = -2\) and \((x_1, y_1) = (0, 0)\).

### 4. Plug in the Values:
\[
y - 0 = -2(x - 0)
\]
This simplifies to:
\[
y = -2x
\]

### Final Equation:
The equation of the line parallel to \( y = -2x + 1 \) that passes through the origin is:
\[
\boxed{y = -2x}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the general form of a linear equation?
2. How do you find the slope of a line from its equation?
3. What does it mean for two lines to be parallel?
4. How would you find the equation of a line perpendicular to \( y = -2x + 1 \)?
5. How does the y-intercept change when you modify the equation of a line?

**Tip:** When finding the equation of a line, always identify the slope first, as it determines how steep the line is.

Learn how to find a line parallel to y = -2x + 1 that passes through the origin (0,0). This problem involves identifying slopes, using the point-slope form of a line equation, and understanding parallel lines in algebra. Suitable for students in Grades 7-9.

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