Question

what is the slope of the linear function described in this table? slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ \

$$\begin{tabular}{|c|c|c|c|c|} \\hline input (x) & 0 & 1 & 2 & 3 \\\\ \\hline output (y) & 9 & 7 & 5 & 3 \\\\ \\hline \\end{tabular}$$

options: $m = 2$, $m = 1/2$, $m = -1/2$, $m = -2$

Explanation:

Step1: Select two points from the table

Let's take \((x_1, y_1) = (0, 9)\) and \((x_2, y_2) = (1, 7)\).

Step2: Apply the slope formula

Using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), substitute the values:
\(m=\frac{7 - 9}{1 - 0}=\frac{-2}{1}=-2\)

Answer:

\(m = -2\) (corresponding to the option with \(m = -2\))