Answer
The x-intercept is $(4,0,0)$
The y-intercept is $(0,-8,0)$
The z-intercept is $(0,0,2)$
We can see a sketch of the plane.
Work Step by Step
$2x-y+4z = 8$
We can find the x-intercept when $y=0$ and $z = 0$:
$2x-y+4z = 8$
$2x-(0)+4(0) = 8$
$x = 4$
The x-intercept is $(4,0,0)$
We can find the y-intercept when $x=0$ and $z = 0$:
$2x-y+4z = 8$
$2(0)-y+4(0) = 8$
$y = -8$
The y-intercept is $(0,-8,0)$
We can find the z-intercept when $x=0$ and $y = 0$:
$2x-y+4z = 8$
$2(0)-(0)+4z = 8$
$z = 2$
The z-intercept is $(0,0,2)$
We can plot these three points on the graph. Then we can connect these three points to sketch the plane for the equation.
