Thank you for the opportunity to help you with your question!

To do these, you have to find the slope of each functions. Which ever functions has the greatest slope has the greatest rate of change.

In the first graph, the slope is rise/run or y2-y1/x2-x2

x y

1 0.5

2 1

3 1.5

Table version of graph 1

Slope = 1.5 -1 / 3-2 = 0.5/1 = 0.5 or 1/2

Function 2 is 2y - 6x = -2 can be rewritten in the y = mx + b

y = -3x - 1

slope is -3 or 3

slope2 = 3 or -3

Function 3 is a table that can be converted to the slope by graphing or using the same slope formula

slope3= y2-y1/ x2-x1 = 3-2/10-7 = 1/3 or 0.3

Of the three slopes found, the second equation has the greatest slope = 3 or -3. Thus, it is the function 2y -6x = -2 with the greatest rate of change.

Please let me know if you need any clarification. I'm always happy to answer your questions.