Answer:
Please check the explanation
Step-by-step explanation:
Given the points
Determining the slope between the points:
![\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(-5,\:-7\right),\:\left(x_2,\:y_2\right)=\left(3,\:1\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-5%2C%5C%3A-7%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%283%2C%5C%3A1%5Cright%29)
![m=\frac{1-\left(-7\right)}{3-\left(-5\right)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1-%5Cleft%28-7%5Cright%29%7D%7B3-%5Cleft%28-5%5Cright%29%7D)
![m=1](https://tex.z-dn.net/?f=m%3D1)
Writing the equation in point-slope form
As the point-slope form of the line equation is defined by
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
Putting the point
and the slope
in the line equation
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
![y-\left(-7\right)=1\left(x-\left(-5\right)\right)\\](https://tex.z-dn.net/?f=y-%5Cleft%28-7%5Cright%29%3D1%5Cleft%28x-%5Cleft%28-5%5Cright%29%5Cright%29%5C%5C)
Hence, the equation in the point-slope form will be:
![y-\left(-7\right)=1\left(x-\left(-5\right)\right)](https://tex.z-dn.net/?f=y-%5Cleft%28-7%5Cright%29%3D1%5Cleft%28x-%5Cleft%28-5%5Cright%29%5Cright%29)
Writing the equation in slope-intercept form
As the point-slope of the equation is
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where m is the slope and b is the y-intercept
Putting m = 1 and (3, 1) to determine the y-intercept
![y = mx+b](https://tex.z-dn.net/?f=y%20%20%3D%20mx%2Bb)
![1 = 1 (3) + b](https://tex.z-dn.net/?f=1%20%3D%201%20%283%29%20%2B%20b)
![1 = 3 + b](https://tex.z-dn.net/?f=1%20%3D%203%20%2B%20b)
![b = -2](https://tex.z-dn.net/?f=b%20%3D%20-2)
so putting
and m = 1 in the slope-intercept form
![y = mx+b](https://tex.z-dn.net/?f=y%20%20%3D%20mx%2Bb)
![y = (1)x + (-2)](https://tex.z-dn.net/?f=y%20%3D%20%281%29x%20%2B%20%28-2%29)
Therefore, the equation in slope-intercept form is:
![y = x -2](https://tex.z-dn.net/?f=y%20%3D%20x%20%20-2)
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 = (1)x + (-2)](https://tex.z-dn.net/?f=y%20%3D%20%281%29x%20%2B%20%28-2%29)
so just simplify the equation to write in standard form
![y = (1)x + (-2)](https://tex.z-dn.net/?f=y%20%3D%20%281%29x%20%2B%20%28-2%29)
![y = x - 2](https://tex.z-dn.net/?f=y%20%3D%20x%20-%202)
![y - x = -2](https://tex.z-dn.net/?f=y%20-%20x%20%3D%20-2)