Question

does this table represent a linear function if so state so and state the slope
x:5, 7
y:-9, -6

Answer 1

To determine if the table represents a linear function, we need to check if the change in \(y\) divided by the change in \(x\) (the slope) is constant.

Given the points:
- \( (5, -9) \)
- \( (7, -6) \)

We can calculate the slope \(m\) using the formula:

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

Here, \( (x_1, y_1) = (5, -9) \) and \( (x_2, y_2) = (7, -6) \).

Calculating the differences:

\[
y_2 - y_1 = -6 - (-9) = -6 + 9 = 3
\]
\[
x_2 - x_1 = 7 - 5 = 2
\]

Now, substituting these values into the slope formula:

\[
m = \frac{3}{2}
\]

Since we have a defined slope between the two points, the table does represent a linear function.

**Conclusion:**
Yes, this table represents a linear function, and the slope is \(\frac{3}{2}\).