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Question

2

4

6

8

y-1-2-3-4-5

A) Do the values in the table above represent a linear function?

Yes, it represents a linear

B) If you said it's a linear function, justify your answer.

*blank*

A Because the x-values increase by 1 as the y-values decrease by 2.

B Because the x-values and y- values need to be increased by the same number.

C Because there is no single pattern between changes in y-values.

D Because the x-values increase by 2 as the y-values decrease by 1.

E Because there is no single pattern between changes in x-values

What is the slope of the line that goes throught the points kn the table

Answer 1

To determine if the values in the table represent a linear function, you can check the change in \( y \) as the change in \( x \) is constant.

A) Do the values in the table above represent a linear function?

Yes, it represents a linear function.

B) If you said it's a linear function, justify your answer.

The correct justification is:

A) Because the x-values increase by 2 as the y-values decrease by 1.

This shows a consistent rate of change, indicating a linear relationship.

Slope Calculation

To find the slope \( m \) of the line through the points in the table, you can use the formula:

\[ m = \frac{\Delta y}{\Delta x} \]

From the values you gave, the changes can be computed as follows:

• \( x \) values: \( 0, 2, 4, 6, 8 \) (change of \( 2 \))
• \( y \) values: \( -1, -2, -3, -4, -5 \) (change of \( -1 \))

Calculating the slope:

For example, using the first two points:

\[ m = \frac{-2 - (-1)}{2 - 0} = \frac{-1 + 1}{2} = \frac{-1}{2} = -0.5 \]

So the slope \( m = -0.5 \). You can check with other pairs of points and you will find that the slope remains consistent.

Thus the slope of the line that goes through the points in the table is \( -0.5 \).