Question

the graph of a function is shown on the coordinate plane below. identify the slope of the function.

Explanation:

Step1: Identify two points

From the graph, we can see that the line passes through \((0, 2)\) and \((-1, 0)\) (or other clear points like \((1, 4)\) as well). Let's take \((x_1, y_1) = (0, 2)\) and \((x_2, y_2) = (-1, 0)\).

Step2: Use slope formula

The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values, we get \(m=\frac{0 - 2}{-1 - 0}=\frac{-2}{-1} = 2\). Alternatively, using \((0,2)\) and \((1,4)\), \(m=\frac{4 - 2}{1 - 0}=\frac{2}{1}=2\).

Answer:

\(2\)