Question

Hey guys! Could someone help me with this problem? I got the wrong answer! The answer is B, but I don’t know how to get it! Could you work it out and explain?! Thank you so much! God Bless!

Answer 1

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:
$m =\frac{y_2-y_1}{x_2-x_1}$
$m = \frac{- \frac{9}{5} - (-2)}{1-0} = \frac{- \frac{9}{5} - ( -\frac{10}{5} )}{1-0}$
$m = \frac{ \frac{1}{5} }{1} = \frac{1}{5}$

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:
$m =\frac{y_2-y_1}{x_2-x_1}$
$m = \frac{-3-0}{0-5} = \frac{3}{5}$

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!