Question

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

$$\begin{tabular}{|c|c|c|c|c|} \\hline input (x) & 0 & 1 & 2 & 3 \\\\ \\hline output (y) & 1 & 4 & 7 & 10 \\\\ \\hline \\end{tabular}$$

$m = 1/3$ $m = 3$ $m = -3$ $m = -1/3$

Explanation:

Step1: Choose two points

We can take the first two points from the table: \((x_1, y_1) = (0, 1)\) and \((x_2, y_2) = (1, 4)\).

Step2: Apply the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substitute the values: \(m=\frac{4 - 1}{1 - 0}\).

Step3: Calculate the slope

Simplify the numerator and denominator: \(m=\frac{3}{1}=3\).

Answer:

m = 3 (corresponding to the option "m = 3")