Final answer:
The line passing through the points (-5,9) and (-6,3) has a slope of 6. Using point-slope form, the equation of the line is y = 6x + 39, which corresponds to Option A.
Step-by-step explanation:
The equation of the line passing through the points (-5,9) and (-6,3) can be found using the formula for the slope (m) which is (y2 - y1)/(x2 - x1). Plugging in our points we get m = (3 - 9)/(-6 - (-5)) which simplifies to m = -6/-1 = 6. This is the slope of the line.
Now that we have the slope, we can use point-slope form which is y - y1 = m(x - x1) to find the equation of the line. Using point (-5,9) and slope 6, we get y - 9 = 6(x - (-5)) which simplifies to y = 6x + 39. Thus, the correct answer is Option A.