Question

Does it matter which coordinate is (x1,y1) and (x2,y2) or can I just choose which coordinate I want it to be?​

Answer 1

Technically not on a graph but on a table yes it matter but here if I were you I would do (2,2) and (-1,-4)

Step-by-step explanation: y=mx+b

(2,2) and (-1,-4) 2=2(2)+b Answer is: y=2x+(-2)

x1 y1 x2 y2 2=4+b

-4-2=-6 -2=b

-1-2=-3 y-intercept

m=2

slope

Answer 2

No, it doesn't matter which coordinate you assign
`(x_1,y_1)` and
`(x_2,y_2)`

Explanation:

Proof

`\textsf{let}\:(x_1,y_1)=(-1,-4)`

`\textsf{let}\:(x_2,y_2)=(2,2)`

`\implies \textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(2-(-4))/(2-(-1))=2`

`\begin{aligned}y-y_1&=m(x-x_1)\\\implies y-(-4) &=2(x-(-1)\\y&=2x-2\end{aligned}`

`\textsf{let}\:(x_1,y_1)=(2,2)`

`\textsf{let}\:(x_2,y_2)=(-1,-4)`

`\implies \textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(-4-2)/(-1-2)=2`

`\begin{aligned}y-y_1&=m(x-x_1)\\\implies y-2 &=2(x-2)\\y&=2x-2\end{aligned}`