Complete the point-slope equation of the line through $(-1,6)$ and $(1,5)$. Use exact numbers. \[ y-6= \]

Step 1 ：Given two points (-1,6) and (1,5), we need to find the point-slope equation of the line passing through these points.

Step 2 ：The point-slope form of a line is given by the formula: \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line.

Step 3 ：The slope of the line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Step 4 ：Substituting the given points into the slope formula, we get \(m = \frac{5 - 6}{1 - (-1)} = -0.5\).

Step 5 ：Substituting the slope and one of the points into the point-slope form, we get the equation of the line: \(y - 6 = -0.5(x - -1)\).

Step 6 ：\(\boxed{y - 6 = -0.5(x + 1)}\) is the point-slope equation of the line through (-1,6) and (1,5).