# The slope of a line - l is -1/3.  Find the equation of a line that is perpendicular to line l?   Please show the working out.

durbanville | Certified Educator

The standard form for a straight line (a linear equation) is

`y=mx+c`

x and y represent points on the line. `m`  is the slope or gradient and `c` is the y-intercept - that is, the point at which the line crosses the y-axis.

We have the slope (also called gradient) of a line - `l` - so we can substitute and instead of m we can replace it with `-1/3` so we can say that `l:`  `y = -1/3 x+c` .We do not have any more information.

Now the rules say that the gradients of perpendicular lines, when they are multiplied, will ALWAYS equal `-1` . This has the same effect as finding the negative reciprocal of the line:

`-1/3 times m = -1`   where `m` is our unknown gradient or slope

`thereforem= -1divide -1/3`

`therefore m = -1 times -3/1`

`therefore m=3` Note how the negatives cancel each other out.

So the equation of the line perpendicular to `l` is

`y= 3x+c`