A line that is perpendicular to another line has a slope that is the opposite reciprocal of the slope of the line it is perpendicular to.
First, we need to find the slope of the line.
slope(m) = y2-y1 / x2-x1
m = -5 - 1 / 2 - 4
m = -6 / -2
m = 3 (neg / neg = pos)
Next, we need to find the y intercept.
To find the y intercept, we plug in what we know into the slope-intercept equation
y=mx+b
y=3x+b (Now we pick one of the coordinates to plug in)
1 = 3(4) + b
1= 12 + b
-12 -12
-11 = b
The y intercept is (0,-11)
The equation of the line is y=3x-11
Remember that the slope of a perpendicular line is the opposite reciprocal of the slope of the line it is perpendicular to
The slope of the perpendicular line is -1/3
The equation of the perpendicular line is
y=-1/3x-11
