What is the x-intercept for the function

Question

What is the x-intercept for the function -12x - y + 7z = 96? Type your answer as a point, (x,y,z),

 

Please help I keep getting fractions for the points! Thank you in advance.

Answer 1

An x-intercept means where does the equation when graphed cross the x-axis? Looking at the equation one can see that when graphed it gives a line in 3-d space. Whenever a line crosses the x-axis, it means that the y & z values must equal 0. Therefore, we must solve for x when y & z both have values of 0. We get:

                                  -12x -y + 7z = 96  original equation

                                  -12x - 0 + 7(0) = 96  substitute y & z with 0

                                  -12x = 96  simplify

                                       x = 96/-12  divide both sides by -12

                                       x = -8  solve for x

The answer is the point (-8,0,0).