Answer : The correct option is, (x-y+1=0)
Step-by-step explanation :
The general form for the formation of a linear equation is:
.............(1)
where,
x and y are the coordinates of x-axis and y-axis respectively.
m is slope of line.
First we have to calculate the slope of line.
Formula used :
![m=\frac{(y_2-y_1)}{(x_2-x_1)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%28y_2-y_1%29%7D%7B%28x_2-x_1%29%7D)
Here,
and ![(x_2,y_2)=(4,5)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%3D%284%2C5%29)
![m=\frac{(5-2)}{(4-1)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%285-2%29%7D%7B%284-1%29%7D)
![m=\frac{3}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3%7D%7B3%7D)
m = 1
Now put the value of slope in equation 1, we get the linear equation.
![(y-y_1)=m\times (x-x_1)](https://tex.z-dn.net/?f=%28y-y_1%29%3Dm%5Ctimes%20%28x-x_1%29)
![(y-2)=1\times (x-1)](https://tex.z-dn.net/?f=%28y-2%29%3D1%5Ctimes%20%28x-1%29)
![(y-2)=(x-1)](https://tex.z-dn.net/?f=%28y-2%29%3D%28x-1%29)
![y-2=x-1](https://tex.z-dn.net/?f=y-2%3Dx-1)
Now rearranging the terms, we get:
![y-x-1=0](https://tex.z-dn.net/?f=y-x-1%3D0)
or,
![x-y+1=0](https://tex.z-dn.net/?f=x-y%2B1%3D0)
From the given options we conclude that the option (x-y+1=0) is an equation of the given line in standard form.
Hence, the correct option is, (x-y+1=0)