Which of the following is a point-slope equation of a line that passes through the points (–1, 4) and (8, –2)?

Slope = (y2-y1)/(x2 -x1)=(-2-4)/(8-(-1)) = -6/9 = -2/3

This slope  have lines be A. and C.
We need to check them.
Point (-1,4)
A. y-4=-2/3(x-1) 
4-4=-2/3*(-1-1)
0=-4/3  False. The line y-4=-2/3(x-1)  does not passes through this point.

C. y-4=-2/3(x+1)
4-4 = - 2/3(-1+1)
0=0 True/ The line y-4=-2/3(x+1) passes through this point.

Answer is C. y-4=-2/3(x+1).