What is the equation of the line passing through (1, –4) and parallel to y = –x + 1?

Step 1: Identify the slope of the given line The equation of the given line is in the form y = mx + c, where m is the slope. Here, m = -1.

Step 2: Understand the property of parallel lines Parallel lines have the same slope. Therefore, the line we are looking for also has a slope of -1.

Step 3: Use the point-slope form of a line The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know that our line passes through the point (1, -4) and has a slope of -1. Substituting these values in, we get:

y - (-4) = -1(x - 1)

Step 4: Simplify the equation Simplify the equation to get it in the form y = mx + c:

y + 4 = -x + 1 y = -x - 3

So, the equation of the line passing through (1, –4) and parallel to y = –x + 1 is y = -x - 3.