In response to: 〜に応えて

〜に応えて means “in response to, to meet” an expectation, a request, encouragement: you act to satisfy what others want. The verb is 応える (こたえる), not to be confused with 答える, which sounds the same but means “to answer a question”. Formal register, common in the press.

• ファンの声援に応えて、選手は大きく手を振った。ふぁんのせいえんにこたえて、せんしゅはおおきくてをふった。In response to the fans' cheers, the player waved enthusiastically.
• お客様の要望に応え、営業時間を夜十時まで延ばしました。おきゃくさまのようぼうにこたえ、えいぎょうじかんをよるじゅうじまでのばしました。In response to customer demand, we've extended our opening hours until 10 p.m.
• 両親の期待に応えられるよう、がんばります。りょうしんのきたいにこたえられるよう、がんばります。I'll do my best to live up to my parents' expectations.
• アンコールに応えて、もう一曲歌った。あんこーるにこたえて、もういっきょくうたった。In response to the calls for an encore, he sang one more song.

応える (こたえる) is “to respond” in the sense of “to react, to satisfy”. 〜に応えて places an action in response to what others expect: their encouragement, their requests, their hopes. The artist comes back on stage in response to the encore; the company changes its hours in response to customers.

There's always a relationship: someone expresses a wish or support, and someone else strives to satisfy it. That's why the expression is so common in press releases and articles.

• 利用者の声に応えて、図書館は日曜日も開くことになった。りようしゃのこえにこたえて、としょかんはにちようびもひらくことになった。In response to users' feedback, the library will now also open on Sundays.
• みなさんのご期待に応えられるよう、全力を尽くします。みなさんのごきたいにこたえられるよう、ぜんりょくをつくします。I'll give it everything I've got to live up to your expectations.

You attach に応えて to a noun expressing an expectation: 期待, 要望, 声, 声援, アンコール, 信頼. に応え is the written continuative form; before a noun, you say に応える. The potential 応えられる is used to say you want to “live up to” something.

• 多くの要望に応える形で、新しいバス路線ができた。おおくのようぼうにこたえるかたちで、あたらしいばすろせんができた。A new bus route was created in response to numerous requests.
• 彼は監督の信頼に応えて、決勝点を決めた。かれはかんとくのしんらいにこたえて、けっしょうてんをきめた。Repaying the coach's trust, he scored the winning goal.

答える (N4), with に, is answering a question, a letter, a call: 質問に答える. 応える (same reading こたえる) is responding to an expectation, through action: 期待に応える. The pronunciation is the same; the meaning tells them apart.

A clue: if you can put “live up to” or “satisfy” after it, it's 応える. If it's “give the answer”, it's 答える.

• インタビューで、記者の質問に答えた。いんたびゅーで、きしゃのしつもんにこたえた。In the interview, he answered the journalist's questions.
• 彼女はみんなの期待に応えて、金メダルを取った。かのじょはみんなのきたいにこたえて、きんめだるをとった。She lived up to everyone's expectations by winning the gold medal.

に応じて (next point) means “depending on, according to”: you adjust something to a variable (年齢に応じて料金が変わる). に応えて is reacting to a request in order to satisfy it. 要望に応じて also occurs (“according to requests, case by case”), but 要望に応えて stresses the response given to a specific request.

• 人数に応じて、部屋の大きさを選べます。にんずうにおうじて、へやのおおきさをえらべます。You can choose the size of the room according to the number of people.
• 地元の声に応えて、祭りが十年ぶりに復活した。じもとのこえにこたえて、まつりがじゅうねんぶりにふっかつした。In response to local wishes, the festival was revived after a ten-year break.