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 =(y_2-y_1)/(x_2-x_1)`

`m = (- (9)/(5) - (-2))/(1-0) = (- (9)/(5) - ( -(10)/(5) ))/(1-0)`

`m = ( (1)/(5) )/(1) = (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 =(y_2-y_1)/(x_2-x_1)`

`m = (-3-0)/(0-5) = (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!