frac{y_{2}-y_{1}}{x_{2}-x_{1}}=k eching

$$\frac { y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } } = k$$

k uchun yechish

$$k=-\frac{y_{2}-y_{1}}{x_{1}-x_{2}}$$

$$x_{2}\neq x_{1}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini -x_{1}+x_{2} ga ko'paytirish.

$$y_{2}-y_{1}=k\left(-x_{1}+x_{2}\right)$$

k ga -x_{1}+x_{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y_{2}-y_{1}=-kx_{1}+kx_{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-kx_{1}+kx_{2}=y_{2}-y_{1}$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-x_{1}+x_{2}\right)k=y_{2}-y_{1}$$

Tenglama standart shaklda.

$$\left(x_{2}-x_{1}\right)k=y_{2}-y_{1}$$

Ikki tarafini x_{2}-x_{1} ga bo‘ling.

$$\frac{\left(x_{2}-x_{1}\right)k}{x_{2}-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$

x_{2}-x_{1} ga bo'lish x_{2}-x_{1} ga ko'paytirishni bekor qiladi.

$$k=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$

x_1 uchun yechish

$$\left\{\begin{matrix}x_{1}=\frac{kx_{2}+y_{1}-y_{2}}{k}\text{, }&y_{2}\neq y_{1}\text{ and }k\neq 0\\x_{1}\neq x_{2}\text{, }&k=0\text{ and }y_{2}=y_{1}\end{matrix}\right,$$