1. \( (-6,-3), m=-1 \) \begin{tabular}{|l|l|l|l|l|l|l|l|l|}\hline & & & & & & & \\ \hline & & & & & & & \\ \hline & & & & & & & \\ \hline & & & & & & & \\ \hline & & & & & & & \\ \hline & & & & & & & \\ \hline & & & & & & \\ \hline & & & & & & \\ \hline & & & & & & & \\ \hline\end{tabular}

To find the equation of a line given a point and a slope, we can use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is a point on the line and \(m\) is the slope. ### Step 1: Identify the known values From the problem, we have: - Point: \((x_1, y_1) = (-6, -3)\) - Slope: \(m = -1\) ### Step 2: Substitute the values into the point-slope formula Substituting the known values into the formula: \[ y - (-3) = -1(x - (-6)) \] This simplifies to: \[ y + 3 = -1(x + 6) \] ### Step 3: Distribute and simplify Now, we will distribute the \(-1\): \[ y + 3 = -x - 6 \] Next, we will isolate \(y\) by subtracting \(3\) from both sides: \[ y = -x - 6 - 3 \] This simplifies to: \[ y = -x - 9 \] ### Final Equation The equation of the line in slope-intercept form is: \[ y = -x - 9 \] This line has a slope of \(-1\) and passes through the point \((-6, -3)\).