Write the equation of the line that goes through the point (-4, 5) and is perpendicular to the given line: y = 4x - 1.?

y = 4x-1 has a slope of 4. The perpendicular has a slope of -1/4.
Point slope equation gives
(y-5) = -1/4(x--4)
y = -x/4 -1 + 5
y = -x/4 + 4

Substitute (-4,5)
5 = --4/4 + 4

Any line can be written in slope-intercept form:
y = mx + b

In this form, m represents the slope and (0,b) represents the y-intercept, where the line crosses the y-axis.

We have a target line:
y = 4x - 1
That means it has a slope of 4.

Two lines are perpendicular if their slopes are negative reciprocals of each other: if a line has slope a/b, its perpendicular has slope -b/a.

So our target line will have a slope that is the negative reciprocal of 4, i.e. -1/4.

Target line's equation:
y = (-1/4)x + b

We now need to solve for b. Fortunately, we have a valid (x,y) in the question: (-4,5). Since that point is on the line, it must satisfy the equation so we can substitute those values in for x and y.

Target line's equation:
y = (-1/4)x + b
(5) = (-1/4)(-4) + b
5 = 1 + b
4 = b

So the equation of our target line in general terms is
y = (-1/4)x + 4

Done. Hope that helps :)