Perpendicular Lines?!?

Question

Write an equation of a line through (4,5) that is perpendicular to y= 1/2x + 3.

How would you do this problem?

Answer 1

given equation is y = 1/2x+3;
It is in the form of y= m x + c; where m is slope of the line.

We know that the slop of the line perpendicular to line y = m x + c is -1/m

according to the given equation the slope of the perpendicular line is -1/m = -2

the equation for the perpendicular line is y = -2 x + c

given that the perpendicular line is passing through point (4,5)

so substituting the point in the line equation, 5 = -2 * 4 + c

c= 13; hence the equation of line perpendicular to given line is

Y = -2 X + 13.

Answer 2

The slope of perpendicular lines have a product of -1

The slope of the line perpendicular to the given line (with slope -1/2) is 2.

The equation is

(y - 5) = 2(x - 4)

Answer 3

Gradient of perpendicular line = - 2
y - 5 = - 2.(x - 4)
y = - 2.x + 13 is equation of perpendicular.

Answer 4

slopes of perpendicular lines are negative reciprocals of each other. in this case, we are looking for negative reciprocal of 1/2 or -2
so:

y - 5 = -2(x - 4)
y - 5 = -2x + 8
y = -2x + 13

Answer 5

your line has gradient 1/2
the perpendicular gradient has to be -2
and it passes through (4,5)
(y-5) = -2(x-4)
y = 13-2x

Answer 6

-2x+13=y slope is the negative inverse to be perpendicular and by pluging (4,5) in equation gives y intercept (0,13)