# Decide whether the data in the table represent a linear function or anexponential function. Explain how you know.хy14-53-14сл

Decide whether the data in the table represent a linear function or an exponential function. Explain how you know.
х
y
1
4
-5
3
-14
сл - IN
-23
-32
A. The data represent an exponential function because there is a
common ratio of 4.
B. The data represent a linear function because there is a common
difference of 9
C. The data represent an exponential function because there is a
5
common ratio of -
D. The data represent a linear function because there is a common
difference of -9.

## This Post Has 12 Comments

1. Expert says:

step-by-step explanation:

2. naenae662 says:

The common difference is same = d = -9

Therefore, the data represent a linear function.

Step-by-step explanation:

Given the table

x                        y

1                         4

2                        -5

3                        -14

4                        -23

5                         -32

Finding the common difference between all the adjacent terms of y-values

d = -5 - 4 = -6,

d = -14 - (-5) = -14+5 = -9

d = -23 - (-14) = -23 + 14 = -9

d = -32 - (-23) = -32 + 23 = -9

It is clear that the common difference between all the adjacent terms is same.

Thus,

d = -9

We know that when y varies directly with x, the function is a linear function.

Here, it is clear that each x value varies 1 unit, and each y value varies -9 units.

i.e. The common difference is same = d = -9

Therefore, the data represent a linear function.

3. Kiki18love says:

A. The data in the table represent a linear function because there is a common difference of -8.

Step-by-step explanation:

Because I just took the test!

4. kamkam6200 says:

a

step-by-step explanation:

5. obedomari says:

D

Step-by-step explanation:

6. dieguezisabel says:

A

Step-by-step explanation:

Answer is a because the common difference is -9

7. kiaunarayne808 says:

Step-by-step explanation:

The data represent a linear function because there is a common difference of -9.

8. angelinagiraffp538zb says:

B) The data represent a linear function because there is a common difference of -9.

Step-by-step explanation:

A linear function is one in which the difference between consecutive y-values is constant.  In this table, to get from one y-value to the next we subtract; this means it is a linear function.

9. lilpeepxliltracy says:

Solution:

1. We will plot the points on the coordinate plane, if they lie in a line it means they are linear.

2. Find the slope between each two points ,if you don't want to plot these points on coordinate plane,then by using the formula of slope between two points which is , =$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ ,if slopes are same between any two points it means these points are collinear.

As you can see in the coordinate plane that these points are not collinear.

Now , $\frac{y}{x}=\frac{\text{First term}}{\text{Second term}}=\frac{162}{54}=\frac{54}{18}=\frac{18}{6}=\frac{6}{2}=3$

It means this is a geometric progression because $\frac{\text{Second term}}{\text{First Term}}=\frac{1}{3}$

Option D : The data represent an exponential function because there is a common ratio of 1/3. is true statement.

$Decide whether the data in the table represent a linear function or an exponential function. explain$

10. Expert says:

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$Which equation can be solved to find x the measure of jk in the diagram?$

11. arivalen says:

D. The data represent an exponential function because there is a common ratio of 1/3.

Step-by-step explanation:

To find a common ratio, find out what the first "y" must be multiplied by to get to the next "y."

162 = 54x

162 ÷ 54 = 3

However, the common ratio is not 3 because the y values are decreasing. The common ratio is 1/3 because 162 × 1/3 = 54.

I hope this helps :))

12. dmgcity says:

B

Step-by-step explanation:

Answer is B because it shows a simple difference of -8