In general the line through (a,b) and (c,d) is
[tex](c-a)(y-b)=(d-b)(x-a)[/tex]
Can you see why?
Here we have
[tex](-6 - -9)(y - -4) = (-2 - - 4)(x- -9)[/tex]
[tex]3(y+4)= 2(x+9)[/tex]
[tex]3y + 12 = 2x + 18[/tex]
[tex]3y = 2x + 6[/tex]
[tex] y = \frac 2 3 x + 2[/tex]
That's choice d, though I would parenthesize it as y=(2/3)x+2 so it doesn't look like we're dividing by x.
