Question

Find the common differences among the x-values and y-values. Then, answer the questions.

(3,0), (6,3),.(9,6), (12,9)

Answer 1

The common difference among the x-values and y-values for the given points (3,0), (6,3), (9,6), (12,9) is 3. This implies that for every increase of 3 in the x-value, there is a corresponding increase of 3 in the y-value, indicating a linear relationship with a slope of 1.

Step-by-step explanation:

To find the common differences among the x-values and y-values for the given points (3,0), (6,3), (9,6), (12,9), we compare consecutive x-values and y-values. First, we take the x-values of the points and subtract the previous x-value from the next x-value:

• 6 - 3 = 3
• 9 - 6 = 3
• 12 - 9 = 3

As we can see, the common difference in x-values is 3. Now, we do the same for the y-values:

• 3 - 0 = 3
• 6 - 3 = 3
• 9 - 6 = 3

Again, the common difference in y-values is also 3. This indicates that for each increase of 3 in x, there is also an increase of 3 in y, implying a linear relationship with a slope of 1.

Answer 2

The common differences among the x-values and y-values is 3

The function represents a linear function

The equation of the function is y = x - 3

Finding the common differences among the x-values and y-values

From the question, we have the following parameters that can be used in our computation:

(3,0), (6,3),.(9,6), (12,9)

The common difference is calculated as follows

x values = 3 - 6 = -3

x values = 6 - 9 = -3

x values = 9 - 12 = -3

y values = 0 - 3 = -3

y values = 3 - 6 = -3

y values = 6 - 9 = -3

Because the common differences are equal, the function is a linear function

A lineat function is represented as

y = mx + c

Using the ordered pairs, we have

3m + c = 0

6m + c = 3

Subtract the equations

6m - 3m + c - c = 3 - 0

3m = 3

m = 1

Calculating c, we have

3 * 1 + c = 0

c = -3

So, we have

y = x - 3

This means that the equation is y = x - 3

Question

Find the common differences among the x-values and y-values. Then, answer the questions.

(3,0), (6,3),.(9,6), (12,9)

Do they represent a linear function

If yes, determine the equation