# How do you find the answer to this question 'Find the equation of a straight line that is perpendicular to the line y=-2x+5 and passes through the point (4,1)?

I know how to find the perpendicular of a line, you just find the gradient, flip it and stick a minus in front of it but i dont know how you would work it out when it says 'that passes through the point (....) so please help

Posted Wed 7th November, 2012 @ 17:13 by Will

1. Work out the gradient. -2*1/2=-1

2. Sub in m and the given values for x and y; x=4, y=1

y=mx+c

1=(1/2)*4+c therefore c=-1

3. Give the gradient m and y-intercept c in the form y=mx+c, multiplying through to simplify.

2y=x+c

Answered Wed 7th November, 2012 @ 20:33 by Alliesweet
Edited by Alliesweet on Wed 7th November, 2012 @ 20:35

Alliesweet is right, just to add on you could also use y-y1=m(x-x1), which i find quicker

just as you said, when you multiply both the gradients we get "-1" as the answer (m1*m2=-1)

therefore the gradient of the perpendicular line in this case is 1/2.

sinse we got the co ordinate where the perpendicular line passes through, we can find the equation of the line usiing (y-Y1)=m(x-X1) by substituting the co ordinates of the point in the place of Y1 & X1.

There it becomes (y-1)=1/2(x-4), we can leave it in this form however if we want to rearrange it, it becomes y-1=x/2-4/2, then y=x/2-2+1

finally we get y=x/2-1

Answered Wed 7th November, 2012 @ 20:44 by Ahamed