The plane y + 4z = 15 intersect which axes?
To determine which axes the plane y + 4z = 15 intersects, we need to find the values of y and z when the other variable (x) is zero.
First, let's focus on the x-axis. To find the intersection of the x-axis and the plane, we need to set x equal to zero and solve for y and z.
When x = 0, the equation becomes y + 4z = 15.
Let's solve it for y:
y + 4z = 15
y = 15 - 4z
Now, let's set y equal to zero and solve for z to find the intersection with the y-axis:
0 + 4z = 15
4z = 15
z = 15/4
So, the plane y + 4z = 15 intersects the x-axis when y = 15 - 4z, and it intersects the y-axis when z = 15/4.
Therefore, the plane intersects the x-axis and the y-axis.