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
-16-16х=21
-16х=21+16
-16х=37
х = -2,3125
<span>2) 12cb</span>²<span>/9bc</span>³ = 4b/3c²
![\frac{12c b^{2} }{9b c^{3} } = \frac{4 b^{2-1} }{3 c^{3-1} } = \frac{4b}{3 c^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B12c+b%5E%7B2%7D+%7D%7B9b+c%5E%7B3%7D+%7D+%3D++%5Cfrac%7B4+b%5E%7B2-1%7D+%7D%7B3+c%5E%7B3-1%7D+%7D+%3D+%5Cfrac%7B4b%7D%7B3+c%5E%7B2%7D+%7D+)
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3) 12ay</span>³<span>/-8a</span>²<span>y = - 3y</span>²/2a
![\frac{12a y^{3} }{-8 a^{2} y} =- \frac{3 y^{3-1} }{2a^{2-1} } =- \frac{3 y^{2} }{2a}](https://tex.z-dn.net/?f=+%5Cfrac%7B12a+y%5E%7B3%7D+%7D%7B-8+a%5E%7B2%7D+y%7D+%3D-+%5Cfrac%7B3+y%5E%7B3-1%7D+%7D%7B2a%5E%7B2-1%7D+%7D+%3D-+%5Cfrac%7B3+y%5E%7B2%7D+%7D%7B2a%7D+)
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4) -6p</span>³<span>q/-12q</span>³ = p³/2q²
![\frac{-6 p^{3} q}{-12 q^{3} } = \frac{ p^{3} }{2 q^{3-1} } = \frac{ p^{3} }{2 q^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B-6+p%5E%7B3%7D+q%7D%7B-12+q%5E%7B3%7D+%7D+%3D+%5Cfrac%7B+p%5E%7B3%7D+%7D%7B2+q%5E%7B3-1%7D+%7D+%3D+%5Cfrac%7B+p%5E%7B3%7D+%7D%7B2+q%5E%7B2%7D+%7D+)
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5) -4ax</span>²<span>/12xy = - ax/3y
</span>
![\frac{-4a x^{2} }{12xy} =- \frac{a x^{2-1} }{ 3y} =- \frac{ax}{3y}](https://tex.z-dn.net/?f=+%5Cfrac%7B-4a+x%5E%7B2%7D+%7D%7B12xy%7D+%3D-+%5Cfrac%7Ba++x%5E%7B2-1%7D+%7D%7B+3y%7D+%3D-+%5Cfrac%7Bax%7D%7B3y%7D+)
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6) 9axy</span>²<span>/6ay</span>³ = 3x/2y
![\frac{9ax y^{2} }{6a y^{3} } = \frac{3x}{2 y^{3-2} } = \frac{3x}{2y}](https://tex.z-dn.net/?f=+%5Cfrac%7B9ax+y%5E%7B2%7D+%7D%7B6a+y%5E%7B3%7D+%7D+%3D+%5Cfrac%7B3x%7D%7B2+y%5E%7B3-2%7D+%7D+%3D+%5Cfrac%7B3x%7D%7B2y%7D+)
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7) 48a</span>²<span>c</span>²<span>/38ac = 24ac/19
</span>
![\frac{48 a^{2} c^{2} }{38ac} = \frac{24*2*a*a*c*c}{19*2*a*c} = \frac{24ac}{19}](https://tex.z-dn.net/?f=+%5Cfrac%7B48+a%5E%7B2%7D++c%5E%7B2%7D+%7D%7B38ac%7D+%3D+%5Cfrac%7B24%2A2%2Aa%2Aa%2Ac%2Ac%7D%7B19%2A2%2Aa%2Ac%7D+%3D+%5Cfrac%7B24ac%7D%7B19%7D+)
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8) 63x</span>³<span>y</span>⁵<span>/84x</span>⁶<span>y</span>⁴ = 3y/4x³
![\frac{63 x^{3} y^{5} }{84 x^{6} y^{4} } = \frac{21*3* y^{5-4} }{21*4* x^{6-3} } = \frac{3y}{4 x^{3} }](https://tex.z-dn.net/?f=+%5Cfrac%7B63+x%5E%7B3%7D++y%5E%7B5%7D+%7D%7B84+x%5E%7B6%7D++y%5E%7B4%7D+%7D+%3D+%5Cfrac%7B21%2A3%2A+y%5E%7B5-4%7D+%7D%7B21%2A4%2A+x%5E%7B6-3%7D+%7D+%3D+%5Cfrac%7B3y%7D%7B4+x%5E%7B3%7D+%7D+)