What is the equation in slope-intercept form of the line that passes through the points (-4,47) and (2,-16)?

Since you're obviously willing to let someone or something do the problem for you, let your linear regression function on your calculator do this. Put the points in a table and ask the calculator to give you the equation of the line. It is faster than asking to do it.

y = -10.5x +5

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If you really want to do this yourself, make use of the 2-point form of the equation for a line.
.. y = (y2 -y1)/(x2 -x1)*(x -x1) +y1
.. y = (-16 -47)/(2 -(-4))*(x +4) +47 . . . . . . plug in the numbers
.. y = -63/6*(x +4) +47 . . . . . . . . . . . . . . . simplify a bit
.. y = (-21/2)x +5 . . . . . . . . . . . . . . . . . . . . put in the desired final form

The answer would be (c)