This problem can be readily solved if we are familiar with the point-slope form of straight lines: y-y0=m(x-x0) ...................................(1) where m=slope of line (x0,y0) is a point through which the line passes.
We know that the line passes through A(3,-6), B(1,2)
All options have a slope of -4, so that should not be a problem. In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.
So we can check which line passes through which point:
a. y+6=-4(x-3) Rearrange to the form of equation (1) above, y-(-6)=-4(x-3) means that line passes through A(3,-6) => ok
b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B ****** this equation is not the line passing through A & B *****
c. y=-4x+6 subtract 2 from both sides (to make the y-coordinate 2) y-2 = -4x+4, rearrange y-2 = -4(x-1) which means that it passes through B(1,2), so ok
d. y-2=-4(x-1) this is the same as the previous equation, so it passes through B(1,2), this equation is ok.
Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
