Which statement explains which function shows a greater rate of change? (1 point) A.) Function 2 shows a greater rate of change, because Richard spends $20 each month and Celina spends $6 each month.
B.) Function 1 shows a greater rate of change, because Celina spends $6 each month and Richard spends $14 each month.
C.) Function 1 shows a greater rate of change, because Celina spends $2 each month and Richard spends −$6 each month.
D.) Function 2 shows a greater rate of change, because Richard spends $6 each month and Celina spends $2 each month.

Well, if you know how to create a linear equation of the form y = mx + b, we can create a second equation based on at least two points of the table.  Let's do that and then compare the rates of change between the two equations.

First...lets construct an equation of form y = mx + b from two X,Y point sets from the table:

(1, 6) and (9, 46) where (X, Y)

the slope formula for the equation is m = y2 - y1/x2 - x1

m = 46 - 6/9 - 1 = 40/8 = 5

The second form of y = mx + b is given by the form:

y - y1 = m(x - x1)

Let's plug that in to get our second equation so we can compare the rates:

y - 6 = 5(x - 1)

y = 5(x - 1) + 6

y = 5x - 5 + 6

y = 5x + 1

Ok, so now we have our second equation/

Let us now pick a number and plug it into x in both equations a couple of times and see what changes more:

Let's pick 4 for the first number

y = -3(4) + 6 = -12 + 6 = -6

Now pick another number to compare

Let's pick 10:

y = -3(10) + 6 = -30 + 6 = -24

The rate of change is (-24) - (-6) = - 18

Now do this for the second equation and then compare the two results:

y = 5x + 1 = 5(4) + 1 = 21

y = 5(10) + 1 = 51

The rate change = (51) - (21) = 51 - 21 = 30

Since 30 is greater on the positive scale then -18 is on the negative scale, then the table values have to have a greater rate of change.  Don't be confused by the negative result from the first set of equations, since in order for them to be EQUALLY OPPOSITE changes we would have to have had

-30 for the first equation and +30 for the second (table) values.

The answer is that the rate of change for the table values is greater then the rate of change for the given equation value.

Step-by-step explanation: