1. ## Perpendicular lines

I can do parallel lines, but not perpendicular

find the equation of the straight line in form ax + by + c = o which:

passes through (1,4) and is perpendicular to 5y = x + 2

thanks

2. Originally Posted by Carl Feltham
I can do parallel lines, but not perpendicular
find the equation of the straight line in form ax + by + c = o which:
passes through (1,4) and is perpendicular to 5y = x + 2
If two lines are perpendicular (neither of them is vertical) then the product of their slopes is -1.
The slope of the given line is $\displaystyle \frac {1}{5}$ so the perpendicular line must have slope $\displaystyle -5$.
Carry on.

3. thanks

4. Originally Posted by Carl Feltham
I can do parallel lines, but not perpendicular

find the equation of the straight line in form ax + by + c = o which:

passes through (1,4) and is perpendicular to 5y = x + 2

thanks
First we need the gradient f the line:

$\displaystyle y = mx + c$

$\displaystyle y = 1/5x + 2/5$

Therefore we now know the gradient of the given line is 1/5.

So the gradient of the perpendicular line must be -5.
Putting this into the equation of the line we are finding, we get:

$\displaystyle y = -5x + c$

$\displaystyle c$ is the y intercept, which is what we will need to find.

$\displaystyle c = y + 5x$

Now, we just need to put the coordinates into the equation to find $\displaystyle c$.

$\displaystyle c = 4 + 5(1)$

$\displaystyle c = 4 + 5$

$\displaystyle c = 9$

We now have our equation

$\displaystyle y = -5x + 9$

(can also be written as: $\displaystyle y = 9 - 5x$)

//j0k3r