Final answer:
To find the point-slope equation for the line, the slope (m) is calculated to be 9, and substituting into the point-slope form with the point (-2, -20), the equation is y + 20 = 9(x + 2).
Step-by-step explanation:
First, we will find the slope (m) of the line that passes through the points (-2, -20) and (9, 79) using the formula m = (y2 - y1) / (x2 - x1). Substituting the points, we get m = (79 - (-20)) / (9 - (-2)) = 99 / 11 = 9. Next, we use the point-slope form of the equation y - y1 = m(x - x1) using the first point (-2, -20) and the calculated slope. Thus, the equation can be written as y - (-20) = 9(x - (-2)), which simplifies to y + 20 = 9(x + 2). Therefore, the point-slope equation for the line is y + 20 = 9(x + 2).