Уравнение прямой y = kx + b
Если прямая проходит через точки (2 ; 1) и (1 ; 0) , то подставим координаты этих точек в уравнение прямой
![\left \{ {{1=2k+b} \atop {0=k+b}} \right.\\\\ \left \{ {{b=-k} \atop {2k-k=1}} \right.\\\\ \left \{ {{k=1} \atop {b=-1}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B1%3D2k%2Bb%7D+%5Catop+%7B0%3Dk%2Bb%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3D-k%7D+%5Catop+%7B2k-k%3D1%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bk%3D1%7D+%5Catop+%7Bb%3D-1%7D%7D+%5Cright.+++)
Уравнение прямой : y =x - 1
Дальше объяснения аналогичные
2) (1 ; 2) (3 ; 4)
y = kx + b
2 = k + b 4 = 3k + b
![\left \{ {{2=k+b} \atop {4=3k+b}} \right.\\\\ \left \{ {{b=2-k} \atop {3k+2-k=4}} \right. \\\\ \left \{ {{b=2-k} \atop {2k=2}} \right. \\\\ \left \{ {{k=1} \atop {b=2-1=1}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2%3Dk%2Bb%7D+%5Catop+%7B4%3D3k%2Bb%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3D2-k%7D+%5Catop+%7B3k%2B2-k%3D4%7D%7D+%5Cright.+%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3D2-k%7D+%5Catop+%7B2k%3D2%7D%7D+%5Cright.+%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bk%3D1%7D+%5Catop+%7Bb%3D2-1%3D1%7D%7D+%5Cright.++)
y = k + b
3) (0 ; 2) (1 ; 0)
![\left \{ {{2=0*k+b} \atop {0=k+b}} \right.\\\\ \left \{ {{b=2} \atop {k=-2}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2%3D0%2Ak%2Bb%7D+%5Catop+%7B0%3Dk%2Bb%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3D2%7D+%5Catop+%7Bk%3D-2%7D%7D+%5Cright.++)
y = - 2x + 2
4) (- 1 ; 2) (2 ; - 1)
![\left \{ {{2=-k+b} \atop {-1=2k+b}} \right.\\\\ \left \{ {{b=k+2} \atop {-1=2k+k+2}} \right. \\\\ \left \{ {{b=k+2} \atop {3k=-3}} \right.\\\\ \left \{ {{k=-1} \atop {b=1}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2%3D-k%2Bb%7D+%5Catop+%7B-1%3D2k%2Bb%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3Dk%2B2%7D+%5Catop+%7B-1%3D2k%2Bk%2B2%7D%7D+%5Cright.+%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3Dk%2B2%7D+%5Catop+%7B3k%3D-3%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bk%3D-1%7D+%5Catop+%7Bb%3D1%7D%7D+%5Cright.+++)
y = - x + 1
5) (0 ; 0) ( - 3 ; - 3)
![\left \{ {{0=0*k + b} \atop {-3=-3k+b}} \right. \\\\ \left \{ {{b=0} \atop {-3k=-3}} \right.\\\\ \left \{ {{b=0} \atop {k=1}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B0%3D0%2Ak+%2B+b%7D+%5Catop+%7B-3%3D-3k%2Bb%7D%7D+%5Cright.+%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3D0%7D+%5Catop+%7B-3k%3D-3%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3D0%7D+%5Catop+%7Bk%3D1%7D%7D+%5Cright.+++)
y = x
6) (1 ; - 2) (- 3 ; - 5)
![\left \{ {{- 2=k+b} \atop {-5=-3k+b}} \right.\\\\ \left \{ {{b=-k-2} \atop {-5=-3k-k-2}} \right.\\\\ \left \{ {{b=-k-2} \atop {-4k=-3}} \right.\\\\ \left \{ {{k=0,75} \atop {b=-2,75}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B-+2%3Dk%2Bb%7D+%5Catop+%7B-5%3D-3k%2Bb%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3D-k-2%7D+%5Catop+%7B-5%3D-3k-k-2%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bb%3D-k-2%7D+%5Catop+%7B-4k%3D-3%7D%7D+%5Cright.%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bk%3D0%2C75%7D+%5Catop+%7Bb%3D-2%2C75%7D%7D+%5Cright.++++)
y = 0,75x - 2,75
1)1,8-3/5=18/10-3/5=12/10=1 2/10=1 1/5
При любом он не имеет решений
1. 50 + 3 * ( 2x - 1 ) = 71
50 + 6x - 3 = 71
6x = 71 - 50 + 3
6x = 24
x = 4