Why shearing multiplying with y?

Question

We know that shear is transformation that distorts the shape of the object. Shear relative to $X-axis$ that is $y=0$ line can be written as: $x'=x+sh_x.y, y'=y$ My question is why $sh_x$ is multiplying by $y,$why not any other constant ? I want to understand intuition behind this. Every book, website don't mention any reason.

Answer 1

This is not a perfect example as things are NOT exactly linear.

Look at a thin tall tree when wind is blowing. The tree will lean (sway) towards one side. The higher the point of tree the more it will move away. So $(x,y)\implies(x+ay, y)$ is the horizontal shear (force acting horizontally), effect will be proportional to the height $(y$ co-ordinate$)$ of the point$.$

Answer 2

A shear mapping represents a similar concept to a lever, where the further the applied force is from the pivot point, the greater the effect, and hence only depends on the perpendicular distance from the shear origin.

Note that beneath the shear line, the direction of the shear is reversed.