When it says 'which has a greater rate of change' it is referring to 'what has a greater slope.' So, let's calculate each thing's slope:
Table:
I'm going to pick the easiest values to work with, so I'll pick the points (0, -2) and (1, -9/5) - I simplified the mixed fraction. So, here we go, the slope formula is:
[tex] m =\frac{y_2-y_1}{x_2-x_1} [/tex]
[tex]m = \frac{- \frac{9}{5} - (-2)}{1-0} = \frac{- \frac{9}{5} - ( -\frac{10}{5} )}{1-0}[/tex]
[tex] m = \frac{ \frac{1}{5} }{1} = \frac{1}{5} [/tex]
So, the table's slope is -1/5.
Graph
We can, again, pick two points. I'll pick the two given: (5, 0) and (0, -3). Let's start off with the same formula:
[tex] m =\frac{y_2-y_1}{x_2-x_1} [/tex]
[tex]m = \frac{-3-0}{0-5} = \frac{3}{5} [/tex]
The graph's slope is 3/5.
Now, we just have to decide which is bigger: -1/5 or 3/5. So, clearly:
3/5 > -1/5.
The 3/5 slope was the graph, hence it has the greater rate of change (that's why it's B). If anything doesn't make sense, feel free to DM me or ask!
