X, y, and z interecepts of a line? (10 points for best explanation)?

Question

If they exist, find the x, y, and z intercepts of the line x=24+7t, y=4+t, z= -20-5t.

(the answer to this was that the x intercept was -4)

how do i get to the answer?

Answer 1

By x intercept, I assume you mean the x-axis. In that case, y and z are both zero. The given line is:

x = 24 + 7t
y = 4 + t
z = -20 - 5t

y = 4 + t = 0
t = -4

Plug in the value for t to see if z = 0 when y = 0.
z = -20 - 5t = 0
-20 - 5(-4) = -20 + 20 = 0

Solve for x when t = -4.
x = 24 + 7t = 24 + 7(-4) = 24 - 28 = -4

The intercept of the x-axis is P(-4, 0, 0).

The line does not intercept the y-axis or z-axis.

Answer 2

My question to you is what do you mean by x intercept,etc ? A line in three space seldom will intersect an axis. The question is generally where does the line intersect the plane where z = 0 ?You would find the parameter value ( t in your case) to make z = 0 . You get (-4,0,0). For the x = 0 plane we see t = -24 / 7 and the point is (0, 4 / 7 , -20 / 7).

Answer 3

first we need to work with something easier so y = 4 + t would be a better choice.

so all the equations x, y, and z all share ' t ', so we need to solve for t. and using the y equation we get:

y - 4 = t

then we plug it into the x equation.

x = 24 + 7( y - 4).

simplify and plug in -4 for x since it's given.

-4 = 24 + 7y - 28

solve for y and get 0.

then solve for z.

so plug in y - 4 for t into the z equation

z = -20 - 5( y - 4 ).
z = -20 - 5y - 20

since we know that y is 0, plug it in.

z = -20 + 20, therefore
z = 0

(x, y, z) = (-4 ,0 ,0) at t = -4

Answer 4

x intercept happens when y and z=0
y=4+t
0=4+t
t=-4

sincex=24+7t
substitute t=-4
x=24+7(-4)
x=-4