≪要点≫
1次関数y=ax+bのグラフの傾きはa,切片はbです. ![]()
右の図はy=2x+1の直線のグラフで,その切片は赤丸で示したy軸との交点のy座標,1です.
(2) これに対して傾きは,y=…の形に書いたときのxの係数ですが,その図形的な意味が分からない生徒が多い.
【例1】
原点(0, 0)を通り,傾きが2の直線 y=2x を図示してください. ![]() 直線の傾きは,右図のように階段状に切り出したときの,縦の長さと横の長さの比,すなわち ![]() そこで,「傾きが2」の直線を描くためには「右に1だけ進んでから,上に2だけ進みます」 ![]() y=−2x のように「傾きがマイナス」の直線を描くには,「右に1だけ進んでから,下に2だけ進みます」 このように,「横の長さ」を1にすると, (傾き)=(縦の長さ)[符号あり]になります.
【要点1】
傾きがa(符号付き)の直線を描くには, ア)傾きaの符号が正のとき
例えばa=2のとき,「右に1進んでから,上に2進む」
イ)傾きaの符号が負のとき
例えばa=−2のとき,「右に1進んでから,下に2進む」
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【例2】
切片が2で,傾きが を図示してください. ![]() 傾きが 直線の傾きは,右図のように階段状に切り出したときの,縦の長さと横の長さの比,すなわち ![]() この問題のように傾きが分数になっている場合は,「右に3進んで上に2進めばよい」. もちろん,
【要点2】
傾きが ア)傾きの符号が正のとき,
例えば
イ)傾きの符号が負のとき
例えば
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【問題1】
次の2段階に分けて,1次関数 (1) 初めに,y軸上で「切片」の場所をクリックしてください.
(2) 傾きが2になるように,もう1つの点をクリックしてください.
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