Answer:
the general form of the equation of the line will be:
![y-x=2](https://tex.z-dn.net/?f=y-x%3D2)
Step-by-step explanation:
Finding the slope:
Taking two points from the line as shown in figure
Finding the slope between (-2, 0) and (0, 2)
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(-2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:2\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-2%2C%5C%3A0%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%280%2C%5C%3A2%5Cright%29)
![m=\frac{2-0}{0-\left(-2\right)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2-0%7D%7B0-%5Cleft%28-2%5Cright%29%7D)
![m=1](https://tex.z-dn.net/?f=m%3D1)
Finding the y-intercept
We know that the y-intercept can be calculated by setting x=0
From the figure, it is clear that at x=0, y=2
Thus, the y-intercept is (0, 2)
We know that the slope-intercept form of the equation line is:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where m is the slope and b is the y-intercept
As we have already determined the slope = m = 1 and the y-intercept b=2.
Substituting the values in the slope-intercept form of the equation line
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
![y=(1)x+2](https://tex.z-dn.net/?f=y%3D%281%29x%2B2)
![y=x+2](https://tex.z-dn.net/?f=y%3Dx%2B2)
Writing the equation in the standard form form
As we know that the equation in the standard form is
![Ax+By=C](https://tex.z-dn.net/?f=Ax%2BBy%3DC)
where x and y are variables and A, B and C are constants
As we already know the equation in slope-intercept form
![y=x+2](https://tex.z-dn.net/?f=y%3Dx%2B2)
so just simplify the equation to write in standard form
![y-x=2](https://tex.z-dn.net/?f=y-x%3D2)
Thus, the general form of the equation of the line will be:
![y-x=2](https://tex.z-dn.net/?f=y-x%3D2)