Question

use the coordinates of the plotted points to complete the calculation below. pay attention to negative signs.

slope = (change in y)/(change in x) = (1 - 2)/(4 - 2)

(graph with points (2, 2) and (4, 1) shown)

Explanation:

Step1: Recall Slope Formula

The slope formula is \( \text{Slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \), where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line. From the graph, the two points are \((2, 2)\) and \((4, 1)\), so \(x_1 = 2\), \(y_1 = 2\), \(x_2 = 4\), \(y_2 = 1\).

Step2: Substitute Values

For the numerator (change in \(y\)): \(y_2 - y_1 = 1 - 2\). For the denominator (change in \(x\)): \(x_2 - x_1 = 4 - 2\). Then calculate the slope: \( \frac{1 - 2}{4 - 2} = \frac{-1}{2} \).

Answer:

\(\frac{-1}{2}\) (or \(-\frac{1}{2}\))