Question

The table below represents a linear function. Identify the slope of the function.
xx yy
00 11
44 minus, 4−4
88 minus, 9−9
1212 minus, 14−14

Answer 1

To find the slope of a linear function given in a table, we can use the formula for the slope (m):

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

From the table, we have the following pairs of points (x, y):

1. (0, 1)
2. (4, -4)
3. (8, -9)
4. (12, -14)

Let's calculate the slope using the first two points (0, 1) and (4, -4):

\[
m = \frac{-4 - 1}{4 - 0} = \frac{-5}{4}
\]

Now, let's verify the slope using the next pair of points (4, -4) and (8, -9):

\[
m = \frac{-9 - (-4)}{8 - 4} = \frac{-9 + 4}{4} = \frac{-5}{4}
\]

Finally, let's check the slope using the points (8, -9) and (12, -14):

\[
m = \frac{-14 - (-9)}{12 - 8} = \frac{-14 + 9}{4} = \frac{-5}{4}
\]

In all cases, the slope is consistent, and we find that the slope of the function is

\[
\boxed{-\frac{5}{4}}
\]