When looking at the piecewise graph for formulas, the first thing I might do is use the magnifying glass with the plus to make it bigger This is obviously a line, it's going to have a y-intercept of four and a slope of... it went down two and over one Down two and over one, so the first part of this is going to be an equation That's going to say y = -2/1x + 4 And this is true when x is greater than 0, but less than or equal to 2 For the second part, we're going to realize that we have two points We have a point here of (2,2). We also have a point over here of (10,0) If I have two points, I should always be able to find the slope So m = (2 - 0) / (2 - 10) The y minus the y over the x minus the x Making sure the top and the bottom are from the same point. So the 2 and 2 were from one point and the 0 and 10 were from one point So we're going to get 2/(-8) or -1/4 is the slope Now we can use the point-slope form that says y - y-value (0) = -1/4 ( x - x-value (10)) I could use either, but always choose to use the one with a zero if I get the chance So we're going to have y = -1/4x + 10/4 by multiplying it out. 10/4 reduces, of course, to 5/2 And this one is only true when x... it's an open dot here, so x needs to be greater than 2 It's a closed dot at the 10, so less than or equal to 10 So when we look at these answers, we're looking for -1/4 x + 5/2 from 2 < x < or = 10 And we're looking for the -2x + 4 between 0 and 2 So if I go back into here and close this out I needed the -2x + 4, so that's going to be my answer C