Final answer:
The point-slope equation of the line given the points (-1, -7) and (2, 5) can be either 'y - 5 = 4(x - 2)' or 'y - (-7) = 4(x - (-1))', corresponding to options (a) and (b) respectively.
Step-by-step explanation:
To write the equation in point-slope form given two points (-1,-7) and (2,5), first, we need to calculate the slope of the line passing through these points. The slope can be calculated using the formula 'slope = (y2 - y1) / (x2 - x1)', where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the slope is (5 - (-7)) / (2 - (-1)) = 12 / 3 = 4.
Then, we can choose either of the two points and the calculated slope to write the point-slope equation of the line. Using point (2,5), the equation is y - 5 = 4(x - 2), which corresponds to option (a) 'y - 5 = 4(x - 2)'. If we use the other point (-1,-7), the equation will be y - (-7) = 4(x - (-1)), which corresponds to option (b) 'y - (-7) = 4(x - (-1))'.