Question

if i have a line y=4x+7. I want to create another line that is perpendicular through point A (16,2). What is the new equation?

Answer 1

Perpendicular lines have the negative reciprocal slope, so the slope of your new line will be -1/4 and the current equation will be as follows:
y = -1/4x + b
(where b is the y intercept)

to find b, plug in point A and you'll get:
2 = -1/4(16) + b
2 = -4 + b
6 = b

the equation will be:
y = -1/4x + 6