To find the equation of the line passing through the points \((-1, 6)\) and \((7, -2)\), you can use the point-slope formula:
\[y - y_1 = m(x - x_1)\]
Where \(m\) is the slope of the line, and \((x_1, y_1)\) are the coordinates of one of the points.
First, find the slope (\(m\)) using the given points:
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
\[m = \frac{(-2) - 6}{7 - (-1)}\]
\[m = \frac{-8}{8}\]
\[m = -1\]
Now that you have the slope (\(m = -1\)), choose one of the points, for example, \((-1, 6)\), and substitute into the point-slope formula:
\[y - 6 = -1(x - (-1))\]
Simplify the equation:
\[y - 6 = -(x + 1)\]
\[y - 6 = -x - 1\]
To express the equation in the standard form (Ax + By = C), move \(x\) and \(y\) terms to the left side and simplify:
\[x + y = 5\]
So, the equation of the line passing through \((-1, 6)\) and \((7, -2)\) is \(x + y = 5\).