the equation has a y intercept and a steadily decreasing value
So that makes it linear (not all linear equations have a y intercept but they do all have a steady increase or decrease)
The y intercept is -6 so we know the equation will have a y intercept of -6
Looking at at graph, we also see for everytime x increases one, that y decreases -3
So that gives the equation a rate of -3x
So the equation is y=-3x-6
So your answer is C