Question

the table of values shows a linear relationship between x and y.
x: -7, -2, 3, 8. y: 9, 1, -7, -15.
what is the slope of the line represented by the table of values

Answer 1

To find the slope of the line represented by the table of values, we can use the formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \):

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

Let's choose two points from the table. We can use the points \( (-7, 9) \) and \( (8, -15) \).

Using these points:

- \( x_1 = -7 \)
- \( y_1 = 9 \)
- \( x_2 = 8 \)
- \( y_2 = -15 \)

Now we substitute the values into the slope formula:

\[
m = \frac{-15 - 9}{8 - (-7)} = \frac{-15 - 9}{8 + 7} = \frac{-24}{15}
\]

Now, simplify the fraction:

\[
m = \frac{-24}{15} = \frac{-8}{5}
\]

Thus, the slope of the line is:

\[
\boxed{-\frac{8}{5}}
\]