your line passes through the point , so you know that (using the standard equation )
Now, let be the intercept of the y-axis, and be the intercept of the x-axis. Then we have . Thus we have and . Since these are intercepts, we can get some more information :
Now recover the equation we found first :
Solving the two equations simultaneously :
And the equation of the line follows :
Plotting this line indeed shows that it passes through , and that this point is exactly midpoint between the x-intercept and y-intercept of the line
Don't hesitate to reply if anything seems confusing.