What is the relationship between the image translation of linear function and X and K?

What is the relationship between the image translation of linear function and X and K?

Generally speaking, we don't consider the relationship with X,
① When k > 0, y increases with the increase of X, that is, the image shows an upward trend; when k < 0, y decreases with the increase of X, that is, the image shows a downward trend
② The relationship between B and B: the value of B determines the intersection of image and Y axis. When b > 0, the image intersects the positive half axis of Y axis; when B < 0, the image intersects the negative half axis of Y axis

Translation problem of function image
After the image of function y = cosx is shifted a unit to the left (0 is less than or equal to a, less than or equal to 2 π), the image of function y = sin (x - π / 6) is obtained, then a =?

The image of y = cosx is y = cos (x + a) when it is shifted a unit to the left,
Because cosx = sin (x + π / 2), it can also be equal to sin (x + π / 2-2 π),
Let cos (x + a) = sin (x + π / 2-2 π + a)
x+π/2-2π+a= x-π/6
（-3/2）π+a=-π/6 ,
a=3π/2-π/6=8π/6=4π/3