Equation of a Plane from Picture

Question

I understand the formula is $ax + by + cz + d$ but don't know how to interpret that from the image.

Answer 1

I'll get you started. Say your plane is defined by the equation $ax+by+cz+d=0$. Then we know that the points $P=(0,0,5),~Q=(0,2,0),~R=(3,0,0)$ are on this plane. Hence, we get the system of equations $$\begin{cases}a(0)+b(0)+c(5)+d=0\\a(0)+b(2)+c(0)+d=0\\a(3)+b(0)+c(0)+d=0\end{cases}$$

Answer 2

For something like that problem the intercept from of the plane equation would be the quickest way to find the equation. https://www.ditutor.com/space/intercept_equation.html

Answer 3

There's a formula, when the axes-intercepts $(a,0,0),\: (0,b,0),\: (0,0,c)$ are given, that every well-bred people should know: $$\frac xa+\frac yb+\frac zc=1.$$