First, let's find the slope of the line using the slope formula, which is:
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
(([tex]x_1[/tex], [tex]y_1[/tex]) and ([tex]x_2[/tex], [tex]y_2[/tex]) are points on the line)
In context of this problem, we can use the formula to find the slope of the line between the two points:
[tex]m = \dfrac{-2 -6}{7 - (-1)} = \dfrac{-8}{8} = -1[/tex]
Now, we can use the slope in the point-slope formula, which will help us find the final equation of the line. (For reference, the point-slope formula is [tex](y - y_1) = m(x - x_1)[/tex] where ([tex]x_1[/tex], [tex]y_1[/tex]) is a point on the line)
In the context of the problem, we could use the formula to find the equation of the line:
[tex](y - 6) = -1(x + 1)[/tex]
[tex](y - 6) = -x - 1[/tex]
[tex]\boxed{y = -x + 5}[/tex]
The equation of the line is y = -x + 5.
