직선의 방정식

두 직선의 위치 관계

1. 두 직선의 위치 관계

평행하다. 일치한다. 한 점에서 만난다.
(1) 평행하다. (2) 일치한다. (3) 한 점에서 만난다. 'data:image/svg+xml;base64,<?xml version="1.0" encoding="utf-8" standalone="no"?>
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'

2. 두 직선의 평행과 수직 조건

  1. 두 직선의 평행 조건
    두 직선 과 에서
    1. 두 직선이 서로 평행하면 이다.
    2. 이면 두 직선은 서로 평행하다.
  2. 두 직선의 수직 조건
    두 직선 과 에서
    1. 두 직선이 서로 수직이면 이다.
    2. 이면 두 직선은 서로 수직이다.

3. 표준형과 일반형으로 표현된 두 직선의 위치 관계

두 직선의
위치 관계		 두 직선의
교점의 개수		 연립방정식의
해의 개수
평행하다.

기울기가 같고 절편이 다르다.		 없다. 없다.(불능)
일치한다.

기울기와 절편이 각각 같다.		 무수히 많다. 무수히 많다.
(부정)
수직이다.
(두 직선의 기울기의 곱) 		한 개 한 쌍
한 점에서
만난다.
기울기가 다르다.
두 직선의<br>위치 관계 {[y=mx+n],[y=m^(')x+n^(')]:} {[ax+by+c=0],[a^(')x+b^(')y+c^(')=0]:} 두 직선의<br>교점의 개수 연립방정식의<br>해의 개수 평행하다. m=m^('),<br>n!=n^(')<br>기울기가 같고 y절편이 다르다. (a)/(a^('))=(b)/(b^('))!=(c)/(c^(')) 없다. 없다.(불능) 일치한다. m=m^('),<br>n=n^(')<br>기울기와 y절편이 각각 같다. (a)/(a^('))=(b)/(b^('))=(c)/(c^(')) 무수히 많다. 무수히 많다.<br>(부정) 수직이다. mm^(')=-1<br>(두 직선의 기울기의 곱)=-1 aa^(')+bb^(')=0 한 개 한 쌍 한 점에서<br>만난다. m!=m^(')<br>기울기가 다르다. (a)/(a^('))!=(b)/(b^('))