1. ![y+2 = 3(x-2)](https://tex.z-dn.net/?f=y%2B2%20%3D%203%28x-2%29)
Point-slope form of the equation of a straight line is:
(1)
The two points in this case are:
![(x_0,y_0)=(2,-2)\\(x_1,y_1)=(5,7)](https://tex.z-dn.net/?f=%28x_0%2Cy_0%29%3D%282%2C-2%29%5C%5C%28x_1%2Cy_1%29%3D%285%2C7%29)
Slope of the line is given by:
![m=\frac{y_1 -y_0}{x_1 -x_0}=\frac{7-(-2)}{5-2}=\frac{9}{3}=3](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_1%20-y_0%7D%7Bx_1%20-x_0%7D%3D%5Cfrac%7B7-%28-2%29%7D%7B5-2%7D%3D%5Cfrac%7B9%7D%7B3%7D%3D3)
Substituting into eq.(1), we find:
![y+2 = 3(x-2)](https://tex.z-dn.net/?f=y%2B2%20%3D%203%28x-2%29)
2. ![y-4 = \frac{3}{4}(x-6)](https://tex.z-dn.net/?f=y-4%20%3D%20%5Cfrac%7B3%7D%7B4%7D%28x-6%29)
Point-slope form of the equation of a straight line is:
(1)
The two points in this case are:
![(x_0,y_0)=(6,4)\\(x_1,y_1)=(2,1)](https://tex.z-dn.net/?f=%28x_0%2Cy_0%29%3D%286%2C4%29%5C%5C%28x_1%2Cy_1%29%3D%282%2C1%29)
Slope of the line is given by:
![m=\frac{y_1 -y_0}{x_1 -x_0}=\frac{1-4}{2-6}=\frac{3}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_1%20-y_0%7D%7Bx_1%20-x_0%7D%3D%5Cfrac%7B1-4%7D%7B2-6%7D%3D%5Cfrac%7B3%7D%7B4%7D)
Substituting into eq.(1), we find:
![y-4 = \frac{3}{4}(x-6)](https://tex.z-dn.net/?f=y-4%20%3D%20%5Cfrac%7B3%7D%7B4%7D%28x-6%29)
3. ![y+3x=3](https://tex.z-dn.net/?f=y%2B3x%3D3)
Standard form of the equation of a straight line is:
![ax+bx=c](https://tex.z-dn.net/?f=ax%2Bbx%3Dc)
with a, b, c integer numbers.
Let's start by finding the point slope form first.
Point-slope form of the equation of a straight line is:
(1)
The two points in this case are:
![(x_0,y_0)=(0,3)\\(x_1,y_1)=(2,-3)](https://tex.z-dn.net/?f=%28x_0%2Cy_0%29%3D%280%2C3%29%5C%5C%28x_1%2Cy_1%29%3D%282%2C-3%29)
Slope of the line is given by:
![m=\frac{y_1 -y_0}{x_1 -x_0}=\frac{-3-3}{2-0}=-\frac{6}{2}=-3](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_1%20-y_0%7D%7Bx_1%20-x_0%7D%3D%5Cfrac%7B-3-3%7D%7B2-0%7D%3D-%5Cfrac%7B6%7D%7B2%7D%3D-3)
Substituting into eq.(1), we find:
![y-3 = -3(x-0)](https://tex.z-dn.net/?f=y-3%20%3D%20-3%28x-0%29)
Now we can re-arrange the equation to re-write it in standard form:
![y-3 = -3(x-0)\\y-3 = -3x\\y-3+3x=0\\y+3x=3](https://tex.z-dn.net/?f=y-3%20%3D%20-3%28x-0%29%5C%5Cy-3%20%3D%20-3x%5C%5Cy-3%2B3x%3D0%5C%5Cy%2B3x%3D3)
4. ![y-x=-2](https://tex.z-dn.net/?f=y-x%3D-2)
Standard form of the equation of a straight line is:
![ax+bx=c](https://tex.z-dn.net/?f=ax%2Bbx%3Dc)
with a, b, c integer numbers.
Let's start by finding the point slope form first.
Point-slope form of the equation of a straight line is:
(1)
The two points in this case are:
![(x_0,y_0)=(1,-2)\\(x_1,y_1)=(4,2)](https://tex.z-dn.net/?f=%28x_0%2Cy_0%29%3D%281%2C-2%29%5C%5C%28x_1%2Cy_1%29%3D%284%2C2%29)
Slope of the line is given by:
![m=\frac{y_1 -y_0}{x_1 -x_0}=\frac{2-(-1)}{4-1}=\frac{3}{3}=1](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_1%20-y_0%7D%7Bx_1%20-x_0%7D%3D%5Cfrac%7B2-%28-1%29%7D%7B4-1%7D%3D%5Cfrac%7B3%7D%7B3%7D%3D1)
Substituting into eq.(1), we find:
![y+1 = x-1](https://tex.z-dn.net/?f=y%2B1%20%3D%20x-1)
Now we can re-arrange the equation to re-write it in standard form:
![y+1=x-1\\y+1-x=-1\\y-x=-2](https://tex.z-dn.net/?f=y%2B1%3Dx-1%5C%5Cy%2B1-x%3D-1%5C%5Cy-x%3D-2)