Hi there!
[tex]\large\boxed{D. \text{ }y = -4x + 6}[/tex]
To derive an equation given the points, we can use the slope formula:
[tex]slope = \frac{y_{2}-y_{1}}{x_{2}-x{1}}[/tex]
Plug in the corresponding coordinates:
[tex]slope = \frac{-6-2}{3-1}[/tex]
Simplify:
[tex]slope = \frac{-8}{2} = -4[/tex]
Therefore, we have:
y = -4x + b
Plug in the x and y values for a coordinate to solve for b:
2 = -4(1) + b
2 = -4 + b
b = 6
The equation is:
y = -4x + 6. The correct answer is D.
