Find an equation for the line with the given properties. Express your answer using either the general form or the​ slope-intercept form of the equation of a line.

Parallel to the line

x - 5y = -2;

containing the point​ (0,0)

To find the equation of the required line, we follow these steps:

### Step 1: Determine the slope of the given line
The given line is:
\[
x - 5y = -2
\]
Rewriting it in slope-intercept form (\(y = mx + b\)):

\[
-5y = -x - 2 \implies y = \frac{1}{5}x + \frac{2}{5}
\]

The slope of the given line is:
\[
m = \frac{1}{5}
\]

Since the required line is parallel to the given line, it has the same slope:
\[
m_{\text{new}} = \frac{1}{5}.
\]

### Step 2: Use the point-slope form of a line
The point-slope form is:
\[
y - y_1 = m(x - x_1),
\]
where \((x_1, y_1)\) is a point on the line. The given point is \((0, 0)\). Substituting \(m = \frac{1}{5}\) and \((x_1, y_1) = (0, 0)\):
\[
y - 0 = \frac{1}{5}(x - 0),
\]
which simplifies to:
\[
y = \frac{1}{5}x.
\]

### Step 3: Express in the desired form
- **Slope-intercept form:** The equation is already in slope-intercept form:
\[
y = \frac{1}{5}x.
\]

- **General form:** Rewrite \(y = \frac{1}{5}x\) in general form (\(Ax + By + C = 0\)):
\[
5y = x \implies x - 5y = 0.
\]

### Final Answer:
The equation of the line is:
\[
y = \frac{1}{5}x \quad \text{or} \quad x - 5y = 0.
\]

Would you like more details on how to rewrite between forms or clarify any steps?

---

### Related Questions:
1. How do you find the equation of a line perpendicular to another given its slope and a point?
2. What are the steps to convert from general form to slope-intercept form of a line?
3. Can you derive the equation of a line from two points?
4. How do parallel lines behave in a coordinate plane?
5. Why does the slope remain constant for parallel lines?

### Tip:
Parallel lines always have the same slope but differ in their \(y\)-intercept unless they coincide.

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. Parallel to the line x - 5y = -2; containing the point (0,0).

Learn how to find the equation of a line parallel to x - 5y = -2 that passes through the point (0,0). This step-by-step solution explains key concepts, including slope-intercept form, general form, and the properties of parallel lines. Perfect for Grades 8-10 students.

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