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43 votes
43 votes
Find the x-intercept of the equation x + 2y + 4z = 6
in the form ( x, y, z)

User Serban
by
2.6k points

1 Answer

17 votes
17 votes

Answer:

(6, 0, 0)

Explanation:

The x-intercept in this context is the point where the plane crosses the y-axis. The values of y and z are both zero there. Filling in those values, we get ...

x +2(0) +4(0) = 6

x = 6

The full set of coordinates for the point will be ...

(x, y, z) = (6, 0, 0)

_____

Additional comment

The equation of the plane in intercept form is ...

x/a +y/b +z/c = 1 . . . . . . . where a, b, c are the x-, y-, z-intercepts

Dividing the given equation by 6 will help you get this form.

x/6 +2y/6 +4z/6 = 1 ⇔ x/6 +y/3 +z/(3/2) = 1

The y-intercept is (0, 3, 0), and the z-intercept is (0, 0, 3/2).

User Artem Novichkov
by
3.4k points