Recently, someone asked about why Vx and Vy change with altitude. This isn't necessarily an easy thing to understand since it involves several variables. So here's a modified "quick" version of the explanation on this topic that is covered in great detail in my “How to Fly an Airplane Handbook.”
Figure 43 shows the power curve vs. rate of climb for three different altitudes. The top of the power curve represents Vy and the tangent’s contact with the power curve represents Vx. The speeds at the bottom of this curve are true airspeeds which makes it easier to represent performance at all altitudes.
Notice that Vy and Vx both increase with an increase in altitude as true airspeeds. Now just ask yourself what indicated airspeeds are necessary to generate the true airspeeds shown for Vx and Vy in Figure 43 (use a 2% increase in TAS for every thousand feet of altitude gain). I’ve done this for you in Figure 49. It’s clear than Vx and Vy converge with altitude when measured as indicated airspeeds.
Clearly Vy increases as a TAS with altitude (Figure 43) but it does so relatively slowly compared to Vx as a TAS. Therefore, Vy as an indicated airspeed can decrease by 1% per thousand feet (Figure 49) while still resulting in the slight increase in Vy as a true airspeed as shown in Figure 43. That’s why the Vy (IAS) line tilts to the left slightly in Figure 49.
To learn more about this and other topics and have fun in the process, check out my "Rod Machado's How to Fly an Airplane Handbook." It covers both basic and advanced flying skills, stick and rudder skills as well as lost flying techniques that are not taught in flight schools today. Learn how to master your airplane by reading this book.