Question

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

$$\begin{tabular}{|c|c|c|c|c|} \\hline input (x) & 0 & 5 & 10 & 15 \\\\ \\hline output (y) & 2 & 3 & 4 & 5 \\\\ \\hline \\end{tabular}$$

$m = 1/5$ $m = -5$ $m = -1/5$ $m = 5$

Explanation:

Step1: Choose two points

Take \((x_1, y_1) = (0, 2)\) and \((x_2, y_2) = (5, 3)\) from the table.

Step2: Apply slope formula

Using \(m=\frac{y_2 - y_1}{x_2 - x_1}\), substitute \(y_2 = 3\), \(y_1 = 2\), \(x_2 = 5\), \(x_1 = 0\). So \(m=\frac{3 - 2}{5 - 0}=\frac{1}{5}\).

Answer:

\(m = \frac{1}{5}\) (corresponding to the option "m = 1/5")