To solve this problem:

We need to write the equation of a line that:

1. Passes through the point $(1, 5)$.
2. Is parallel to the line $y = -4x + 2$.

Step 1: Recall the slope of parallel lines

Parallel lines have the same slope. From the equation $y = -4x + 2$, the slope ($m$) is $-4$.

Step 2: Use the point-slope form

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Here, $(x_1, y_1)$ is the given point $(1, 5)$, and $m = -4$.

Substitute the values: $y - 5 = -4(x - 1)$

Step 3: Simplify the equation

Distribute $-4$: $y - 5 = -4x + 4$

Add 5 to both sides: $y = -4x + 9$

Final Answer:

The equation of the required line is: $y = -4x + 9$

Would you like further details or clarifications?

Here are 5 related questions to deepen your understanding:

1. How do you determine the slope of a line from its equation?
2. What would the equation be if the line passed through a different point, like $(2, 7)$?
3. How do you find the equation of a line perpendicular to a given line?
4. What is the geometric significance of parallel lines having the same slope?
5. How do you convert between slope-intercept form and point-slope form?

Tip:

Always check if the given point satisfies your final equation to ensure correctness!