Question

The slope of the function is
x: 0,3,6,9
y: 5.5 11.5 17.5, 23.5

Answer 1

To find the slope of the function defined by the given points, we can use the slope formula:

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

We have the following points based on your data:

- \( (0, 5.5) \)
- \( (3, 11.5) \)
- \( (6, 17.5) \)
- \( (9, 23.5) \)

We can calculate the slope using the first two points:

Let \( (x_1, y_1) = (0, 5.5) \) and \( (x_2, y_2) = (3, 11.5) \).

\[
\text{slope} = \frac{11.5 - 5.5}{3 - 0} = \frac{6}{3} = 2
\]

Thus, the slope of the function is \( 2 \).

To confirm that the slope is consistent across all pairs of points, we can check another pair, say \( (3, 11.5) \) and \( (6, 17.5) \):

Let \( (x_1, y_1) = (3, 11.5) \) and \( (x_2, y_2) = (6, 17.5) \).

\[
\text{slope} = \frac{17.5 - 11.5}{6 - 3} = \frac{6}{3} = 2
\]

And checking the last pair, \( (6, 17.5) \) and \( (9, 23.5) \):

Let \( (x_1, y_1) = (6, 17.5) \) and \( (x_2, y_2) = (9, 23.5) \).

\[
\text{slope} = \frac{23.5 - 17.5}{9 - 6} = \frac{6}{3} = 2
\]

Since the slope is consistently \( 2 \) for all pairs of points, we can conclude that the function has a constant slope of \( 2 \).