A line /ell passes through the points B (7,-1) and C(1,7). The equation of this line can be written in the form y=mx+b compute m+b.
The point-slope form of a line is y-y_1=m(x-x_1), where a point is (x_1, y_1). The slope of our line is (7-(-1))/(1-7) = -4/3. Thus, we may input (1,7) into y-y_1 = -4/3(x-x_1), getting y-7 = -4/3(x-1), so y=-4/3x + 4/3 + 7 = -4/3x + 25/3.
m+b = 7