1. Write an equation of the line that passes through the point P

and is perpendicular to the line with the given equation:
P(1,4); y = -2x + 4
answer y= 2 x + 2

2. Write an equation of the line that passes through the point P
and is perpendicular to the line with the given equation:
P(5,3); y = 5x + 2
answer y= 5x + 28

1 answer

No, for both

The slopes of perpendicular lines are negative reciprocals of each other.
that is, you have to change the sign and flip the fraction
for your first one:
slope of -2 turns into a slope of +1/2
for the second the slope of +5 turns into -1/5
(a slope of -3/4 would turn into a slope of 4/3)

back to the first one ...
your new line would be y = (1/2)x + b
plug in the given point (1,4)
4 = (1/2)(1) + b
b = 4 - 1/2 = 7/2

new equation: y = (1/2)x + 7/2

redo the 2nd in the same way