O. Find the equation of the line passing through the points whose coordinates are \( P_{1}(-4,13) \) and \( P_{2}(-1,1) \).

To find the equation of the line passing through the points \( P_{1}(-4,13) \) and \( P_{2}(-1,1) \), we first need to calculate the slope (m) of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the coordinates, we get: \[ m = \frac{1 - 13}{-1 - (-4)} = \frac{-12}{3} = -4 \] Now that we have the slope, we can use the point-slope form of the line equation: \[ y - y_1 = m(x - x_1) \] Using point \( P_1 \): \[ y - 13 = -4(x + 4) \] Expanding and rearranging gives us the equation of the line: \[ y = -4x - 16 + 13 \] \[ y = -4x - 3 \] So, the equation of the line is \( y = -4x - 3 \). To graph this line, start by identifying the y-intercept (where it crosses the y-axis), which is at the point (0, -3). From there, use the slope of -4 to find another point; for every 1 unit you move to the right (increasing x), you'd move down 4 units (decreasing y). This gives you a clear path to sketch the line!