By "Hull, Options, Futures, and Other Derivatives":
Suppose that, in figure,the stock price is \$100 and the option price is \$10. Imagine an investor who has sold 20 call option contracts—that is, options on 2,000 shares. The investor’s position could be hedged by buying $0.6 \times 2,000 =1,200 $ shares. The gain (loss) on the stock position would then tend to offset the loss (gain) on the option position.
For example, if the stock price goes up by \$1 (producing a gain of \$1,200 on the shares purchased), the option price will tend to go up by $0.6 \times \$1 = \$0.60$ (producing a loss of \$1,200 on the options written);
Why the option price that will tend to go up by \$ 0.60, produce a loss of \$1,200?
If strike price $K= \$ 50$, we have that investor loss:
$$(\$ 100 - \$ 50 ) \times 2,000 = \$ 100.000$$
If the stock price goes up by $1, the investor loss:
$$(\$ 101 - \$ 50 ) \times 2,000 = \$ 102.000$$
so, if the stock price goes up by \$1, the option contract produce a loss of \$ 2.000