Question

what does the slope of the line tell you about the situation?
the bins weight decreases by 100 pounds for every box packed.
the bins weight decreases by 10 pounds for every box packed.
the bin weighs 200 pounds after 50 boxes are packed.
the bin weighs 700 pounds before any boxes are packed.

Explanation:

The slope of a line in a context relating the number of boxes packed (x - axis) and the bin's weight (y - axis) represents the rate of change of the bin's weight with respect to the number of boxes packed. A negative slope (since weight is decreasing as boxes are packed) would tell us how much the weight decreases per box. The option "The bin's weight decreases by 10 pounds for every box packed" is about the rate of change (slope), while the other options either describe a specific point (like weight after 50 boxes or initial weight) which are related to the y - intercept or a point on the line, not the slope. Wait, no, let's re - evaluate. Wait, if we consider the slope formula \(m=\frac{\Delta y}{\Delta x}\), where \(\Delta y\) is the change in weight and \(\Delta x\) is the change in the number of boxes. If the slope is - 10, that would mean for each increase of 1 in \(\Delta x\) (each box packed), \(\Delta y\) (weight) decreases by 10. The first option says decreases by 100, which would be a slope of - 100. But the key is that the slope is the rate of change of weight per box. So the option "The bin's weight decreases by 10 pounds for every box packed" is the one that describes the slope (rate of change), while the other options: "The bin weighs 200 pounds after 50 boxes are packed" is a point on the line (when x = 50, y = 200), "The bin weighs 700 pounds before any boxes are packed" is the y - intercept (when x = 0, y = 700), and the first option is a different rate. So the correct one related to slope (rate of change per box) is "The bin's weight decreases by 10 pounds for every box packed".

Answer:

The bin's weight decreases by 10 pounds for every box packed.