Write an equation in slope-intercept form for the line perpendicular to y=−4x+1 that passes through the point (−7,1).

y = (1/4)x + (11/4)

Step-by-step explanation:

A perpendicular line equation has a slope that is the negative inverse of the reference line, in this case y = -4x + 1.

This means we want a new that that has a slope of -(-1/4) or (1/4).

That leads to:

y = (1/4) + b

Any value of b will still yield a straight, but perpendicular line.  But the question is more particular, like a difficult spouse.  It wants to go through the point (-7,1).  We can make that happen by setting a value for by that will move the line such that it crosses (-7,1).  Substitute that point in the equation and solve for b:

y = (1/4)x + b

1 = (1/4)(-7) + b

b = 1 +(7/4)

b = (4/4 + 7/4)

b = (11/4)

The equation becomes y = (1/4)x + (11/4)

See attachment.