Question

find slope of table
x 2,5,8,11,14
y -2,-6,-10,-14,-18

Answer 1

To find the slope of the relationship between \( x \) and \( y \) from the given values, we can use the slope formula:

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

Choose any two points from the table. Let's use the first two points, \( (2, -2) \) and \( (5, -6) \):

- \( x_1 = 2 \), \( y_1 = -2 \)
- \( x_2 = 5 \), \( y_2 = -6 \)

Now substitute these values into the slope formula:

\[
\text{slope} = \frac{-6 - (-2)}{5 - 2} = \frac{-6 + 2}{5 - 2} = \frac{-4}{3}
\]

Thus, the slope of the line represented by the table is \(-\frac{4}{3}\).

You can verify the slope using other points from the table and will arrive at the same slope since the values indicate a linear relationship.