Answer:
![3x - y = - 2](https://tex.z-dn.net/?f=3x%20-%20y%20%3D%20%20-%202)
Step-by-step explanation:
The given line PQ passes through the points P(-5,-13) and Q(5,17) .
Find the slope using the formula:
![m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20)
Plug in the points to get:
![m = \frac{17 - - 13}{5 - - 5}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B17%20-%20%20-%2013%7D%7B5%20-%20%20-%205%7D%20)
![m = \frac{30}{10}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B30%7D%7B10%7D%20)
![m = 3](https://tex.z-dn.net/?f=m%20%3D%203)
Use the point-slope formula :
![y-y_1 = m(x - x_1)](https://tex.z-dn.net/?f=y-y_1%20%3D%20m%28x%20-%20x_1%29)
Substitute the point (5,17)
![y - 17 = 3(x - 5)](https://tex.z-dn.net/?f=y%20-%2017%20%3D%203%28x%20-%205%29)
Expand:
![y - 17 = 3x - 15](https://tex.z-dn.net/?f=y%20-%2017%20%3D%203x%20-%2015)
The standard form is when the equation is put in the form
![ax + by = c](https://tex.z-dn.net/?f=ax%20%2B%20by%20%3D%20c)
Regroup the terms to get:
![3x - y = - 17 + 15](https://tex.z-dn.net/?f=3x%20-%20y%20%3D%20%20-%2017%20%2B%2015)
The standard form is
![3x - y = - 2](https://tex.z-dn.net/?f=3x%20-%20y%20%3D%20%20-%202)