I'm trying to solve this question which has left me stumped. The previous part of the question gave us this graph:
It asked to quickly guess what is the linear equation of the line which passes through both $(0,3)$, $(0,0)$, which is immediately $x=0$.
Right after, as if to use that question as direction, we are asked, once again, to quickly guess the equation for a plane which passes through $(9,0,0), (0,5,0)$, and $(0,0,3)$. I don't know how to guess this immediately without having to calculate the system of equations to get $5x+9y+15z=45$.
What am I missing? What intuition have I failed to carry over from the previous question?
Note that the plane intersects with the $x, \>y, \> z$-axis at $9,\>5, 3$, respectively. Thus, the equation takes the form $$\frac x9+\frac y5 + \frac z3 =1$$