Is that the correct spelling of "like"?

"So I met this guy, he's gay, and I was so disappointed when I finally met him," said the woman on the train, "He's gay,  but like, faux-gay, like, he didn't want to do my hair or go shopping. I'm like, what's the point? I thought I was going to set him up with Brendan, but then I was like no way! I know!" 

"Wow," I thought to myself, "This is a woman who is in no way prejudiced or biased. She doesn't let heuristics get in the way of sound thinking. Every gay man is a caricature of the one seen on TV, and that's the only reason they're valuable. I can't believe he didn't want to do her hair!" I was composing the courage to tell her to go make me a sandwich, but she got off at the next stop.