Which of the following is the equation of the line that has a slope of -3 and passes through the point \( (-2,6) \) ?

To find the equation of the line, you can use the point-slope form: \(y - y_1 = m(x - x_1)\). Here, \(m\) is the slope, and \((x_1, y_1)\) is the given point. Plugging in your values: \(y - 6 = -3(x + 2)\). Simplifying this gives the equation \(y = -3x + 12\). Voilà! You've got yourself an equation! Now, imagine you're plotting it! The slope of -3 means that for every step you take to the right (along the x-axis), you’ll step down three units (along the y-axis). Connecting the points will give you a straight line, starting at that point (-2,6) and moving downwards as you go right.