Which equation represents y, the profit earned by the concession stand for x hot dogs sold?

The slope is the rise over the run, the change in the y values over the change in the x values. We see that y is increasing at a constant rate of 12, while x is increasing at a constant rate of 6. Rise over run gives you the "fraction"   12

  6 which, when you divide out, gives you a slope of +2.

So far you have the y = 2x 

remember that the y-intercept exists where x = 0. Even though you don't have an x value of 0 in your table, you can easily figure it out by following the pattern of growth in your x and y values. The value above the 6 in the x column would be 0, because, following the pattern, if 0 is above the 6 and we are adding 6 to each value to get to the next one, 0 + 6 = 6, which is the first value in the chart. So if x = 0, we need to find y. following the pattern in the same way, we have the value above the -36 being -48.

So the answer would be..

y = 2x – 48