Find the gradient of the line 4x+9y=10.

There are two approaches to this problem.

Firstly, you could rearrange the equation so that you have the general equation of a line, y=mx+c, where m is the gradient that you are looking for! When we rearrange the equation, we get y=-4/9x+10/9 so the gradient is -4/9.

Also, we can use implicit differentiation to get the solution. We do this by differentiating both sides of the equation with respect to x. This gives us 4+9dy/dx=0. This can be rearranged to give dy/dx=-4/9. As we know the first derivative is the gradient - we can say the gradient of the line is -4/9.