Final answer:
Calculating the slope for the given points (-6, 8) and (3, -7) gives us -5/3, and using the point-slope form yields the equation y = (-5/3)x - 2, which does not match any of the provided choices.
Step-by-step explanation:
To find the equation of the line in slope-intercept form with the given two points (-6, 8) and (3, -7), we first need to calculate the slope (m). The slope is defined as the ratio of the change in y to the change in x between two points on a line, which is:
m = (y2 - y1) / (x2 - x1)
Using the given points (-6, 8) and (3, -7), we calculate the slope as follows:
m = (-7 - 8) / (3 - (-6)) = -15/9 = -5/3
With the slope, we can use the point-slope form, y - y1 = m(x - x1), to find the equation of the line. Substituting one of the points (-6, 8) into the equation, we get:
y - 8 = (-5/3)(x - (-6))
Expanding this, we have:
y - 8 = (-5/3)x - (-5/3)(-6)
y - 8 = (-5/3)x - (-10)
Now we add 8 to both sides to get:
y = (-5/3)x - 10 + 8
y = (-5/3)x - 2
Therefore, none of the given choices a), b), c), or d) matches the correct slope-intercept form of the line, which is y = (-5/3)x - 2.