Answer:
x - 4y = 0 . . . in standard form
y = (1/4)x . . . in slope-intercept form
Step-by-step explanation:
The slope of the given line is ...
m = (y2 -y1)/(x2 -x1) = (9 -(-7))/(-1 -3) = 16/-4 = -4
The slope of the perpendicular line is the negative reciprocal of this:
desired slope = -1/m = -1/-4 = 1/4
This can be used in the point-slope form of the equation of a line:
y -h = m(x -k) . . . . . line with slope m through point (h, k)
Your perpendicular line has a slope of 1/4 and goes through point (4, 1), so its equation can be written as ...
y -1 = (1/4)(x -4)
y = (1/4)x -1 +1
y = (1/4)x
In standard form, this is ...
4y = x
x -4y = 0
