CPM Homework Help : A2C Problem 7-21

For each of the following equations, find every point where its three-dimensional graph intersects one of the coordinate axes. That is, find the x-, y- and z-intercepts. Express your answer in (x, y, z) form. .

$6y + 15z = 60$

Hint (a):

To find the intercept of a given axis, set all other variables to zero.
For example, the y-intercept will be $\left(0, ?, 0\right)$ .
To find the y-intercept, let $x = 0$ and $z = 0$

more help (a):

Repeat the process to find the z-intercept. $\left(0, 0, ?\right)$ .

answer (a):

$\left(0, 10, 0\right)$ and $\left(0, 0, 4\right)$

$3x + 4y + 2z = 24$

Hint (b):

See part (a):

$\left(x + 3\right)^{2} + z^{2} = 25$

Hint (c):

See part (a).
Note: You will have two x-intercepts and two z-intercepts. Why

$z = 6$

Hint (d):

See part (a):

Use the eTool below to test your solutions to parts (a), (b) and (c) above.
Click the link at right for the full version of the eTool: 7-21 HW eTool