Question

x= 2.6 y= -6
x= 3.2 y= 3
Determine the rate of change of the linear function given as a table of values.
(1 point)
m = 0.067
m = 15
m = -5
m = -15

Answer 1

To determine the rate of change (slope) of the linear function, we can use the formula for slope \( m \):

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

Using the given points \( (x_1, y_1) = (2.6, -6) \) and \( (x_2, y_2) = (3.2, 3) \):

1. Calculate \( y_2 - y_1 \):
\[
y_2 - y_1 = 3 - (-6) = 3 + 6 = 9
\]

2. Calculate \( x_2 - x_1 \):
\[
x_2 - x_1 = 3.2 - 2.6 = 0.6
\]

3. Now substitute these values into the slope formula:
\[
m = \frac{9}{0.6}
\]

4. Calculate \( m \):
\[
m = 15
\]

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