A line passes through the point $(-9,1)$ and has a slope of -2 . Write an equation for this line.

Step 1 ：The equation of a line in slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 2 ：We know the slope \(m\) is -2, and we know that the line passes through the point \((-9,1)\). We can substitute these values into the equation to solve for \(b\).

Step 3 ：Substituting \(m = -2\) and the point \((-9,1)\) into the equation gives us \(1 = -2(-9) + b\). Solving for \(b\) gives us \(b = -17\).

Step 4 ：Now that we have the value of \(b\), we can substitute \(m\) and \(b\) back into the equation \(y = mx + b\) to get the equation of the line.

Step 5 ：Substituting \(m = -2\) and \(b = -17\) into the equation gives us \(y = -2x - 17\).

Step 6 ：Final Answer: The equation of the line is \(\boxed{y = -2x - 17}\).