Learn Swedish: Vilken tur att bilen kan bogseras gratis! - What luck that the car can be towed for free!

This is the passive infinitive, which is exactly what we need after the modal verb kan ("can"). To form it, you take the base infinitive bogsera ("to tow") and simply add an -s to the end. While kan bogsera means "can tow" (active), kan bogseras means "can be towed" (passive).

Why does the sentence use Vilken tur instead of Vad tur for "What luck"?

In Swedish exclamations, you use vilken, vilket, or vilka directly before a noun. Since tur is an en-word noun, we use vilken (literally: "Which luck!"). You only use vad in exclamations right before an adjective or an adverb, such as in Vad bra! ("How good!").

How would this sentence look if we used the active form instead of the passive bogseras?

To use the active form, you have to introduce a subject—someone who is actually doing the towing. You could use the general pronoun man ("one"/"they") and say: Vilken tur att man kan bogsera bilen gratis! The beauty of the passive bogseras is that it lets us focus entirely on the car without needing to mention the tow truck driver.

Does the word gratis change its ending if the noun is plural or an ett-word?