Answer:
![y - 6 = -2(x-1)](https://tex.z-dn.net/?f=y%20-%206%20%3D%20-2%28x-1%29)
Step-by-step explanation:
Given; The graph above
Required: Equation of line AB (in point slope form)
First, we need to determine the slope of the graph;
From the graph; we can observe that when y = 6, x = 1 and when y = 2, x = 3
Such that
![(x_1, y_1) = (1,6)\\(x_2, y_2) = (3,2)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%281%2C6%29%5C%5C%28x_2%2C%20y_2%29%20%3D%20%283%2C2%29)
The slope of a line is define as thus;
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![m = \frac{2 - 6}{3 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2%20-%206%7D%7B3%20-%201%7D)
![m = \frac{-4}{2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-4%7D%7B2%7D)
![m = -2](https://tex.z-dn.net/?f=m%20%3D%20-2)
Considering only point
; The slope is define as thus
![m = \frac{y - y_1}{x - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By%20-%20y_1%7D%7Bx%20-%20x_1%7D)
Substitute
and ![(x_1, y_1) = (1,6)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%281%2C6%29)
![-2 = \frac{y - 6}{x - 1}](https://tex.z-dn.net/?f=-2%20%3D%20%5Cfrac%7By%20-%206%7D%7Bx%20-%201%7D)
Multiply both sides by x - 1
![-2(x-1) = \frac{y - 6}{x - 1} (x-1)](https://tex.z-dn.net/?f=-2%28x-1%29%20%3D%20%5Cfrac%7By%20-%206%7D%7Bx%20-%201%7D%20%28x-1%29)
![-2(x-1) = y - 6](https://tex.z-dn.net/?f=-2%28x-1%29%20%3D%20y%20-%206)
Rearrange
![y - 6 = -2(x-1)](https://tex.z-dn.net/?f=y%20-%206%20%3D%20-2%28x-1%29)
Hence, the equation of the line is a point slope form is ![y - 6 = -2(x-1)](https://tex.z-dn.net/?f=y%20-%206%20%3D%20-2%28x-1%29)