Answer
The x-intercept is $(6,0,0)$
The y-intercept is $(0,3,0)$
The z-intercept is $(0,0,6)$
We can see a sketch of the plane.
Work Step by Step
$x+2y+z = 6$
We can find the x-intercept when $y=0$ and $z = 0$:
$x+2y+z = 6$
$x+2(0)+(0) = 6$
$x = 6$
The x-intercept is $(6,0,0)$
We can find the y-intercept when $x=0$ and $z = 0$:
$x+2y+z = 6$
$(0)+2y+(0) = 6$
$y = 3$
The y-intercept is $(0,3,0)$
We can find the z-intercept when $x=0$ and $y = 0$:
$x+2y+z = 6$
$(0)+2(0)+z = 6$
$z = 6$
The z-intercept is $(0,0,6)$
We can plot these three points on the graph. Then we can connect these three points to sketch the plane for the equation.
