Find the y-intercept (which is b) ; Perpendicular to y = 3x - 1 (which has the negative reciprocal of the slope) ; passes through (6, -16) which will help us find b :)
Our first step is to locate the slope, which is "m" in slope intercept form.
As you can see, we are given an equation that is already in slope intercept form, so simply locate "m"
y = 3x - 1
Slope 1 = 3 (as it is in the "m" spot) Slope 2 = -1/3 (as it is the negative reciprocal)
Now that we have our slope, plug in the slope (-1/3) and (6, -16) into our new slope intercept equation so that we can find the value of "b" which is our y-intercept.
y = mx + b
(-16) = -1/3(6) + b
Simplify.
-16 = -2 + b
Add 2 to both sides.
-16 + 2 = b
Simplify.
-14 = b → Therefore, our y-intercept is -14 → THAT IS OUR FINAL ANSWER - however, if you'd like to know the final equation including the y-intercept, here it is :)
Now that we have all of the needed information, simply plug everything in! :)
