Final answer:
The equation of the line that passes through (1, 2) and is parallel to the line 4x + y - 1 = 0 is y = -4x + 6.
Step-by-step explanation:
To find the equation of the line that passes through (1, 2) and is parallel to the line 4x + y - 1 = 0, we need to determine the slope of the given line. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept.
The given line 4x + y - 1 = 0 can be rewritten in the slope-intercept form as y = -4x + 1. Since parallel lines have the same slope, the slope of the line we're looking for is -4.
Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can substitute the values (1, 2) and -4 for x1 and m, respectively, to find the equation of the line. Plugging in the values, we get y - 2 = -4(x - 1). Simplifying the equation gives us y = -4x + 6, which is the equation of the line that passes through (1, 2) and is parallel to 4x + y - 1 = 0.