using the coordinates of the given point, then determine the value of b.

To find the equation of the line, we first need to find the slope of the line. The slope (m) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Let's use the coordinates (-4,8) and (2,-1) to calculate the slope:

m = (-1 - 8) / (2 - (-4))
= (-9) / 6
= -3/2

Now that we have the slope (-3/2), we can substitute it along with one of the given points (let's use (-4,8)) into the slope-intercept form of a linear equation:

y = mx + b

8 = (-3/2)(-4) + b
8 = 6 + b
b = 8 - 6
b = 2

Therefore, the value of b is 2. The equation of the line is:

y = (-3/2)x + 2