If you are given a graph, an equation, and a table; each representing a different linear function how would you determine which one has the greatest rate of change

you would simply calculate the slope for each, a graph it is easy because you simply get two points on the graph and solve for it (y2-y1/x2-x1), an equation if it is in slope intercept form, the coefficient of x is the slope, from a table you use a similar method to a graph except you grab two values/instances, let's say in a table the numbers are presented like this:

3   4

2   6

You would then simply do the same thing for solving for the slope (y2-y1/x2-x1). In this instance it would be 6-2/4-3=4/1

All of these would give you the rate of change as the slope is the rate of change.

Step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

definitely a. the others have almost all data points on one side of the line.

step-by-step explanation: