Animating line thickness and length

I'd like to create a line that gets fatter as it lengthens from left to right, but I want the previous thicknesses to remain unchanged, so at full length it will look kind of like a stretched out triangle (one pixel on the left, 25 pixels on the right). I've tried combining the stroke width property with the trim path property, but that fattens the entire line as it grows (see attachment), not the effect that I want.

I realize I could draw the final shape and reveal it with an animated mask, but I was hoping to do it just with properties for simplicity. Is there a way?