We are asked to find the equation of a line that is parallel to the given line $y = -2x + 5$ and passes through the point $C(3, 6)$. Since the lines are parallel, they will have the same slope.

Step-by-step solution:

1. Identify the slope of the given line: The equation $y = -2x + 5$ is in slope-intercept form $y = mx + b$, where $m$ is the slope. So, the slope of the given line is $-2$.

2. Use the point-slope form of the equation of a line: The equation of a line that passes through a point $(x_1, y_1)$ with slope $m$ is given by: $y - y_1 = m(x - x_1)$ Here, the slope $m = -2$ and the point is $(3, 6)$.

3. Substitute the values into the point-slope form: $y - 6 = -2(x - 3)$

4. Simplify the equation: $y - 6 = -2x + 6$ $y = -2x + 6 + 6$ $y = -2x + 12$

Final equation:

$y = -2x + 12$

This is the equation of the line parallel to $y = -2x + 5$ that passes through the point $(3, 6)$.

Do you want more details or have any questions?

Here are 5 related questions:

1. How do we find the equation of a line perpendicular to a given line through a specific point?
2. What is the difference between the point-slope form and the slope-intercept form of a line?
3. How can we verify if two lines are parallel just by looking at their equations?
4. How can we convert the equation of a line from point-slope form to standard form?
5. How do we find the equation of a line passing through two given points?

Tip: When two lines are parallel, they always share the same slope, but they differ in their y-intercept values!