Final answer:
To find the equation of the perpendicular line to y=4x+1, we use the negative reciprocal of the original slope, which is -1/4, and the point (-4,0) to yield y=(-1/4)x+1.
Step-by-step explanation:
To find the equation of a line perpendicular to the given line y = 4x + 1, we first note that the slope of this line is 4. For a line to be perpendicular, its slope must be the negative reciprocal of 4, which is -1/4. Now, using the point-slope form of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line, we substitute (-4,0) for (x₁, y₁) and -1/4 for m.
The equation becomes:
y - 0 = (-1/4)(x - (-4))
y = (-1/4)x + 1, after simplifying.
So, the equation of the perpendicular line is y = (-1/4)x + 1.