Final answer:
An equation can be used to describe the intersection of an object with each of the coordinate planes. To describe the intersection with the x-axis, set the y-coordinate and z-coordinate to zero in the equation. To describe the intersection with the y-axis, set the x-coordinate and z-coordinate to zero in the equation. To describe the intersection with the z-axis, set the x-coordinate and y-coordinate to zero in the equation.
Step-by-step explanation:
An equation can be used to describe the intersection of an object with each of the coordinate planes. Let's consider a 3-dimensional Cartesian coordinate system with the x-axis, y-axis, and z-axis representing the coordinate planes. The x-axis represents the horizontal plane, the y-axis represents the vertical plane, and the z-axis represents the depth plane.
To describe the intersection with the x-axis (horizontal plane), we set the y-coordinate and z-coordinate to zero in the equation, resulting in an equation in terms of x only. Similarly, to describe the intersection with the y-axis (vertical plane), we set the x-coordinate and z-coordinate to zero in the equation. Lastly, to describe the intersection with the z-axis (depth plane), we set the x-coordinate and y-coordinate to zero in the equation.
For example, if we have an object described by the equation y = 2x + 3z, the intersection with the x-axis would be given by the equation y = 0 + 3z, which simplifies to y = 3z. The intersection with the y-axis would be given by the equation 2x + 3(0) = 0, which simplifies to 2x = 0, and the intersection with the z-axis would be given by the equation 2x + 3z = 0.