Aparticle moves along the curve below. y = 24 + x3 as it reaches the point (1, 5), the y-coordinate is increasing at a rate of 4 cm/s. how fast is the x-coordinate of the point changing at that instant?

Now, before we continue, I want to stress the importance of what dy/dt and dx/dt actually mean.

When we're dealing with time, space, and movement along a one-directional plane, we're moving with two scalar quantities (using our parametric representation of a particle), namely its x-direction and its y-direction.

Thus, by differentiating x with respect to t, we're literally saying: "well, what is the change of rate of x in relation to time", or "as t moves along the plane, what is the change of rate of x in that time?"

This can be stressed for the y-ordinate, as well.

So, the change of rate of the y-ordinate (dy/dt is 4cm/s). This is how fast the vertical quantity is changing as time changes at that point.

I’m going to infer you said parallel.solve for yy= -1/2x+7/4lines that are parallel have the same slope, different y intercept.so we know m is -1/2then from there solve for y intercept.