Question

HELP ASAP I'M FAILING AND I DON'T UNDERSTAND THIS

1. The equation of a plane in space is 8x + 6y + 3z = 24. a.) Find each of the intercepts using the equation above and fill out the table below. Make sure you give each intercept as a point in 3-Space:
x-intercept
y-intercept
z-intercept

Answer 1

The intercept can be found when all other variables are equated to zero.
x-intercept when y = 0 and z = 0: 8x + 6*0 + 3*0 = 24 gives x = 3
y-intercept when x = 0 and z = 0: 8*0 + 6y + 3*0 = 24 gives y = 4
z-intercept when x = 0 and y = 0: 8*0 + 6*0 + 3z = 24 gives z = 8

The intercepts are (3, 0, 0), (0, 4, 0), and (0, 0, 8).