Question

The table represents a linear function.

What is the slope of the function?

A: –10
B: –5
C: 5
D: 10

Answer 1

pick 2 sets of points from ur table...

(-4,-16)(-2,-6)
slope = (y2 - y1) / (x2 - x1)
slope = (-6 - (-16) / (-2 - (-4) = (-6 + 16) / (-2 + 4) = 10/2 = 5

u could pick any 2 of ur sets of points.....it will come out the same...let me show you...
(2,14)(4,24)
slope = (y2 - y1) / (x2 - x1)
slope = (24 - 14) / (4 - 2) = 10/2 = 5...see, it is the same no matter what 2 sets of points u choose)

Answer 2

The slope of the linear function is 5, indicating a consistent rate of change. Therefore, the correct answer is C: 5.

To determine the slope of the linear function represented by the table, select two points, such as (-4, -16) and (4, 24).

Apply the slope formula:
`\(\text{Slope} = \frac{\text{Change in } y}{\text{Change in } x}\)`.

Substituting values, the slope is
`\((24 - (-16))/(4 - (-4)) = (40)/(8) = 5\)`.

Consequently, the slope of the function is 5. This indicates that for every unit increase in the independent variable x, the dependent variable y increases by 5 units.

Thus, the correct answer is C: 5. The linear function has a consistent rate of change, and the slope remains the same regardless of the specific points chosen for calculation.