How does a change in altitude effect TAS assuming Mach Number remains constant?

I don't know - what happens to the speed of sound as ALT changes?

Speed of sound changes with air temp. - with air temp decrease, the speed of sound decreases. At higher altitudes the air density and pressure ratio is lowered, along with temp. so speed of sound decreases with altitude as well.
EX: standard day @sea level, 59F' speed of sound is 661 knots. (density and pressure ratio is equal to 1.0)
At 35000 ' temp is roughly -60 degreesF, density and pressure ratio's drop below 1.0 and speed of sound is now 576 knots.