Phương trình đường thẳng đi qua điểm I(3,-1) và song song với đường thẳng \(2 x-3 y=5\)

Gọi (d) là đường thẳng cần tìm

Ta có 

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfKttLearuGlw5gvP1wzaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakqaabeqaaiabbkdaYiabbccaGiabbIha4jabb2caTiab % bodaZiabbccaGiabbMha5jabb2da9iabbwda1aqaaiabgsDiBlabbo % daZiabbMha5jabb2da9iabbkdaYiabbIha4jabb2caTiabbwda1aqa % aiabgsDiBlabbMha5jabb2da9maalaaabaGaeGOmaiJaemiEaGNaey % OeI0IaeGynaudabaGaeG4mamdaaaqaaiabgsDiBlabdMha5jabg2da % 9maalaaabaGaeGOmaidabaGaeG4mamdaaiabdIha4jabgkHiTmaala % aabaGaeGynaudabaGaeG4mamdaaaaaaa!6384! \begin{array}{l} {\rm{2 x - 3 y = 5}}\\ \Leftrightarrow {\rm{3y = 2x - 5}}\\ \Leftrightarrow {\rm{y = }}\frac{{2x - 5}}{3}\\ \Leftrightarrow y = \frac{2}{3}x - \frac{5}{3} \end{array}\)

(d) song song với đường thẳng \(y=\frac{2}{3} x-\frac{5}{3}\) nên phương tình đường thẳng (d): \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfKttLearuGlw5gvP1wzaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakeaacqWG5bqEcqGH9aqpdaWcaaqaaiabikdaYaqaaiab % iodaZaaacqWG4baEcqGHRaWkcqWGIbGyaaa!431B! y = \frac{2}{3}x + b\)

Lại có:

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfKttLearuGlw5gvP1wzaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakqaabeqaaiabdMeajnaabmaabaGaeG4mamJaei4oaSJa % eyOeI0IaeGymaedacaGLOaGaayzkaaGaeyicI4SaemizaqMaeyO0H4 % 9aaSaaaeaacqaIYaGmaeaacqaIZaWmaaGaeiOla4IaeG4mamJaey4k % aSIaemOyaiMaeyypa0JaeyOeI0IaeGymaedabaGaeyi1HSTaeGOmai % Jaey4kaSIaemOyaiMaeyypa0JaeyOeI0IaeGymaedabaGaeyi1HSTa % emOyaiMaeyypa0JaeyOeI0IaeG4mamdaaaa!5E79! \begin{array}{l} I\left( {3; - 1} \right) \in d \Rightarrow \frac{2}{3}.3 + b = - 1\\ \Leftrightarrow 2 + b = - 1\\ \Leftrightarrow b = - 3 \end{array}\)

Vậy phương trình đường thẳng (d): 

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfKttLearuGlw5gvP1wzaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakqaabeqaaiabdMha5jabg2da9maalaaabaGaeGOmaida % baGaeG4mamdaaiabdIha4jabgkHiTiabiodaZaqaaiabgsDiBlabdM % ha5jabg2da9maalaaabaGaeGOmaiJaemiEaGNaeyOeI0IaeGyoaKda % baGaeG4mamdaaaqaaiabgsDiBlabiodaZiabdMha5jabg2da9iabik % daYiabdIha4jabgkHiTiabiMda5aqaaiabgsDiBlabikdaYiabdIha % 4jabgkHiTiabiodaZiabdMha5jabg2da9iabiMda5aaaaa!6161! \begin{array}{l} y = \frac{2}{3}x - 3\\ \Leftrightarrow y = \frac{{2x - 9}}{3}\\ \Leftrightarrow 3y = 2x - 9\\ \Leftrightarrow 2x - 3y = 9 \end{array}\)