Question

Which equation is graphed here?

Answer 1

You can find the slope of this line directly from the graph.  The "run" from -2 to 0 is 2, and the "rise" (actually, a drop) from 4 to 1 is -3.  Thus, the slope is -3/2.

Eliminate the 2nd answer possibility; its slope is wrong.

The point-slope form of the eq'n of a str line is

y-k = m(x-h)             Compare this to the first answer possibility:
                                y + 5 = -3/2(x - 4).  Recognize that k= -5 and h=4.
                                Check:  does the point (4,-5) lie on the given line?
                                Yes.  Thus, this is the correct formula.