Question

Use the table to answer the question. This table has the x and y values that will contribute to determining the rate of change and the initial value of the linear function. x y 2.6 −6 3.2 3 Determine the rate of change of the linear function given as a table of values. (1 point) Responses m=−5 m equals negative 5 m=−15 m equals negative 15 m=0.067 m equals 0.067 m=15

Answer 1

To determine the rate of change (slope) of the linear function given the points (2.6, -6) and (3.2, 3), we can use the formula for the slope \( m \) of a line, which is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, we can use the points:

• \( (x_1, y_1) = (2.6, -6) \)
• \( (x_2, y_2) = (3.2, 3) \)

Now substituting these values into the formula:

\[ m = \frac{3 - (-6)}{3.2 - 2.6} = \frac{3 + 6}{3.2 - 2.6} = \frac{9}{0.6} \]

Now, calculate the slope:

\[ m = \frac{9}{0.6} = 15 \]

Therefore, the rate of change \( m \) of the linear function is m = 15.