Find the equation of the line passing through the point (1, 4) and perpendicular to the line y = 5x - 9. y=?

Question

Find the equation of the line passing through the point (1, 4) and perpendicular to the line y = 5x - 9. y=?

Answer 1

If a line is perpendicular to another, that means that their slopes are opposite reciprocals of each other.

Since the slope of the given line is 5, the slope of the 2nd line is -1/5.

We're given a point the 2nd line passes through, so we have an x, y, and m.  Now we can solve for b:

y = mx + b

4 = (-1/5)(1) + b

4 = -1/5 + b

4 + 1/5 = b

21/5 = b

So your equation is:

y = (-1/5)x + 21/5

Answer 2

the slope of this line should be the negative inverse of f(x), so a=-(1/5), We now have the equation y=-(1/5)x+b, Substitute in the co-ordinates and you get 4=-(1/5)1+b

4=(-1/5)+b

b=4.2

So I think it is y=(-1/5)x+4.2

Answer 3

perpendicular to the line y = 5x - 9

m= -1/5

the line passing through the point (1, 4):

4=-1/5*1+q

q= 21/5

the equation is:

y= -1/5x +21/5

or

x+5y-21=0