2) (3 points) Find the equation of the line that passes through the point $(-2,-11)$ and is perpendicular to the line that passes through the points $(1,1)$ and $(5,-1)$.

Step 1 ：Understand the problem: We are asked to find the equation of a line that passes through a given point and is perpendicular to another line.

Step 2 ：Find the slope of the line passing through the points (1,1) and (5,-1) using the formula \((y2 - y1) / (x2 - x1)\). So, the slope of the line passing through the points (1,1) and (5,-1) is \((-1 - 1) / (5 - 1) = -2 / 4 = -1/2\).

Step 3 ：Find the slope of the line perpendicular to the above line. The slope of a line perpendicular to a line with slope m is \(-1/m\). So, the slope of the line perpendicular to the line with slope -1/2 is \(-1 / (-1/2) = 2\).

Step 4 ：Find the equation of the line using the formula \(y = mx + b\), where m is the slope and b is the y-intercept. We know the slope (m = 2) and a point on the line (-2, -11). We can substitute these values into the equation to find the y-intercept (b). So, \(-11 = 2*(-2) + b\), \(-11 = -4 + b\), and \(b = -11 + 4 = -7\).

Step 5 ：So, the equation of the line is \(y = 2x - 7\).

Step 6 ：Check the solution: The line \(y = 2x - 7\) passes through the point (-2, -11) and is perpendicular to the line that passes through the points (1,1) and (5,-1), so the solution is correct.

Step 7 ：The final answer is \(\boxed{y = 2x - 7}\).