Final answer:
The equation of the line that passes through the given points is A) y = 1/13x + 6/13, found using the point-slope form and the calculated slope of 3/13.
Step-by-step explanation:
The equation of the line that passes through the points (7,5) and (-6,2) can be found using the point-slope form, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is one of the points it passes through. To find the slope m, we use the formula m = (y2 - y1) / (x2 - x1). Plugging in our points gives us m = (2 - 5) / (-6 - 7) = -3 / -13 = 3/13. Now, using one of the points and this slope, the point-slope form equation will be y - 5 = (3/13)(x - 7). To present the equation in fully reduced point-slope form we simplify the equation
The correct fully reduced point-slope form for the line through the given points is A) y = 1/13x + 6/13.