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To solve this problem, we need to find the equation of a line that passes through the point \( A(0, 6) \) and is parallel to the line \( y = 5x \).

### Step-by-Step Solution:

1. **Determine the slope of the given line:**
   The equation of the line is given as \( y = 5x \). This is in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope. Here, \( m = 5 \).

2. **Find the slope of the parallel line:**
   Since the required line is parallel to \( y = 5x \), it will have the same slope, \( m = 5 \).

3. **Use the point-slope form to find the equation:**
   The point-slope form of a line's equation is:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope. For our problem, \( (x_1, y_1) = (0, 6) \) and \( m = 5 \).

   Substituting these values, we get:
   \[
   y - 6 = 5(x - 0)
   \]

   Simplify this to:
   \[
   y - 6 = 5x
   \]
   \[
   y = 5x + 6
   \]

4. **Determine the correct answer:**
   The equation we found is \( y = 5x + 6 \), which corresponds to option **C**.

### Final Answer:
The correct answer is **C) y = 5x + 6**.

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Would you like more details, or do you have any other questions? Here are some related questions you might be interested in:

1. What is the general formula for the slope of a line between two points?
2. How do you determine if two lines are perpendicular?
3. How can you find the equation of a line given two points?
4. What is the difference between the point-slope form and the slope-intercept form of a line's equation?
5. How do you find the y-intercept of a line if you have its slope and a point on it?

**Tip:** When two lines are parallel, they have the same slope.

La ecuación de la recta que pasa por el punto A(0, 6) y es paralela a y = 5x es:

Solve for the equation of a line passing through point A(0, 6) and parallel to y = 5x. This problem explores key concepts of linear equations and the property of parallel lines having equal slopes. Suitable for students in Grades 8-10.

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