In the gradient descent algorithm say $f(x)$ (quadratic function) is the objective function. SO the algorithm is defined as
$x_i = x_i - a\frac{\partial f(x)}{\partial x_i}$
I Just dont quite understand the meaning of doing a subtraction. I'm intuitively able to follow that we are going in the direction of steepest descent but have some questions. The derivative of $f(x)$ is going to give us the equation of a line. So when we substitute the value of $x_i$ in $f'(x)$ , what we get is a $y$ coordinate: $y_i$. So I dont understand how we subtract a $y$ coordinate from an $x$ coordinate ?