Final answer:
The intercepts of the equation 2x + 5y - 4z = 40 are (20, 0, 0), (0, 8, 0), and (0, 0, -10).
Step-by-step explanation:
To find the intercepts of the equation 2x + 5y - 4z = 40, we set one variable to zero and solve for the remaining variables. Starting with the x-intercept, we set y = 0 and z = 0 and solve for x. Substituting these values, we get 2x = 40, which gives x = 20. Therefore, the x-intercept is (20, 0, 0).
Next, we find the y-intercept by setting x = 0 and z = 0. Substituting these values, we get 5y = 40, which gives y = 8. Therefore, the y-intercept is (0, 8, 0).
Finally, we find the z-intercept by setting x = 0 and y = 0. Substituting these values, we get -4z = 40, which gives z = -10. Therefore, the z-intercept is (0, 0, -10).
Learn more about Intercepts of a linear equation