# What is the the Cartesian equation of the plane having x-, y-, and z-intercepts of 2, 5, and 3 respectively?

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Should be known by heart: if the $x$, $y$ and $z$_intercepts are $a,\ b,\ c$ ($\neq 0$) respectively, an equation is $$\frac xa+\frac yb+\frac zc=1.$$

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### nalyhs

Updated on July 23, 2022

Write the general equation $ax + by + cz = 1$ and substitute $(2, 0, 0)$ for $(x, y, z)$.
The general equation is $ax+by+cz=k$. What values can you choose for $a$, $b$ and $c$ so that you get the same result for $(x,y,z)$ equal to $(2,0,0)$, $(0,5,0)$ and $(0,0,3)$?