Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to firstname.lastname@example.org and Uncle Colin will do what he can.
Dear Uncle Colin,
I've got a line with equation $10y+36x=16.5$. That equation has no negative numbers in it, yet its gradient is apparently negative. I don't understand why.
-- Silly Line, Only Positive Equation
It looks like we're in misconception-land! In fact, you can write the equation of any line without negative signs by simply rearranging the equation so that everything is positive. I don't recommend it, though: it's generally a better idea to rearrange it into a form that gives you the gradient directly. In particular, the trick here is to isolate $y$ as follows:
$10y + 36x = 16.5$ -- now subtract $36x$ from both sides:
$10y = -36x + 16.5$ --1 then divide by 10:
$y = - 3.6x + 1.65$ --2 Now do you see a -3.6?
When written in $y=mx+c$ form3, the number in front of the $x$ gives the gradient of the line. You could also get the gradient by differentiating, but that's a story for another day.
-- Uncle Colin