WEBVTT

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このビデオでは
直線の（一次関数の）方程式を

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傾き切片型で表す練習を
たくさんやっていこうと思います

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まず おさらいですが
傾き切片型とは 直線の方程式が

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y = mx + b で表されている型のことで
m は傾き

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b は y 切片です

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では たくさんの問題をやっていきましょう

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この問題は 
直線の傾きが -5 だと言っているので

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m は -5 です

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そして y 切片は 6 ですから

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b は 6 です

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なので これはかなり簡単ですね

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この直線の方程式は

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y = -5x + 6 です

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そんなに難しくなかったですね

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では 次の問題をやってみましょう

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この直線の傾きは -1 で
また 直線は 点 ( 4/5 , 0 )

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を含んでいる

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傾きは -1 だと言っていますから

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m は -1 だと既にわかっています

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でも y 切片はまだ分かっていません

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それで この直線の方程式は
傾き m が -1 ですから

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y = -1x + b で表すことができます
まだ判明していない切片を

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b で表しています

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ここで直線はある点を含んでいるということが分かっていて

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その点の座標が与えられていますから

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その情報を使って b を求めます

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直線がこの点を含んでいるというのはつまり

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x = 4/5 , y = 0 が
直線の方程式を満たしている

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ということです

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ではこれらを代入しましょう
x が 4/5 の時

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y は 0 です

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すると 0 = -1 ・ 4/5 + b 
となって

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少し下にスクロールしましょう

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すると
0 = -4/5 + b となるので

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方程式の両辺に 4/5 を足して

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こちらに 4/5 を足して

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こちらにも 4/5 を足します

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4/5 を両辺に足したそもそもの理由は
この -4/5 をなくすためです

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すると b = 4/5 となります

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これで方程式を書くことができます

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y イコール -- 
-1 x は単に -x とします

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b は 4/5 ですから
y = -x + 4/5 です

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では次の問題にいきましょう

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直線は
点 (2,6) と (5,0) を含んでいる

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この問題では傾きも切片も
明確には与えられていません

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ですがこれらの数の組を使って
傾きと切片を求めることができます

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まず最初に傾きを求めましょう

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傾きとは (yの変化量) 割る (xの変化量)ですから

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y の変化量はどれだけですか？

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こちら側から始めましょう

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6 ひく 0

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分かりやすいように

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色分けしていきます

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6 ひく 0 
が y の変化量です

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x の変化量は
2 ひく 5 です

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なぜ色分けしたかというと
どちらからどちらを引くのか

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みなさんに分かりやすく示すためです
このように 最初に黄色の y を持ってきたら

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x も黄色を最初に持ってこないといけない

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黄色で書いたのは
点 (2,6) を表していて

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こちらは
点(5,0) を表しています

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この 2 と 5 をひっくり返して引くことはできません

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そうすると答えの正負が逆になってしまいます

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さてどうなるでしょう

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6 引く 0 は 6 で

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2 引く 5 は -3 ですから

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- 6/3 それはつまり

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-2 と同じことです

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これがこの直線の傾きです

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これまでに分かったことを使って直線の方程式を表すと

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y = -2x +b

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