Next, look at the slope-intercept form of a line in 2D, y=mx+b, and describe which labels in 3D for a line relate to m and b.
In the slope-intercept form of a line in 2D, y = mx + b, m represents the slope of the line and b represents the y-intercept, i.e., the point where the line intersects the y-axis.
In 3D, a line can be represented using parametric equations such as:
x = x0 + at
y = y0 + bt
z = z0 + ct
Here, (x0, y0, z0) is a point on the line, and (a, b, c) are the direction ratios or direction vector components of the line.
The concepts of slope and y-intercept from 2D algebra do not have direct analogs in the 3D parametric equation form because, in 3D, we have three axes (x, y, and z-axis) and a line can have different orientations and relationships with these axes. However, you can think of the direction ratios (a, b, c) as being somewhat similar to the slope in a 2D equation, as they determine the direction and angle of the line in 3D space. The point (x0, y0, z0) can be thought of as an analog to the y-intercept (b), as it is a point where the line intersects a plane in 3D space.